page 693 and the continuation from class notes on 2/21/09.
Factorial formula for permulations
order is important, permulations or arrangements
Permuladtions: type of arrangements=group
formula: nPr=n!
(n-r)! as a denominator
n1 objects taken r object at a time, the total # of arrangements is called total # of arrangements,
1. cannot repeat
2. order is important
for example:
10 peole
randomly are to be selected from for a 3 member committee,
3-member committee
president
Vice president
Secretary
the combinations can only be in a certain order.
ABC
BAC
formula:
10P3=10! as the numerator and
(10-3)! as the denominator= 10! over 10times 9 times 8 times 7!
7!= 7! then cancel out the 7 = 720 ways. choices.
Combination method: page 693
(objects) n taken r
as a group at a time
total number of combinations is n! over =nCr
r!(n-r)!
example for combination:
10 people
choose a 3 member committee
from a rotating committed where everyone is equal
choose 3 people from 10 for equal, how many ways.
formula is in fraction form.
10!
over 3! (10-3)!
no order only as a groups
=10!=10 times 9 times 8 times 7
over 3!= 3! and 7! because 10-3=7
cancel then calculate=
the 7's cancel in both the nominator and in the denominator
then multiple
10 times 9 times 8 times
over 3 times 2 = 120
review the pascal triangle
know page 712
table 8
n(AUB)=
Friday, February 27, 2009
Mathematical Concepts 115 ch. 11 continued
Notes on chapter 11 continued:
ex. 2
How many intergers between 1000, and 9999 divisible by 5 has 4 digits.
10 digits from 10-100.
9,10,10,2, only choose from 0-5 or two choices.
9 is 1-9, 10 is 0-9 choices,
the product rule is 9 times 10 times 10 times 10, times 2 = 1800
2. second rule: formula: factorial
0!=1
n!=1 times 2-n
1!=1
2!=1 times 2 =2
3!=1 times 2 times 3=6
4!=1 times 2 times 3 times 4 = 24
3rd rule: Factorial rule and the product rule:
example 3.
3 places or 3 boxes =
3 times 2 times 1 = 6
3 places to put people.
Arrangements of n distinct objects page 688
n=n1,+ n2, + .....nk
ex. 20 cards some cards may have 20 letters.
5 A
6 B
3 C
6 D
how many different ways to arrange the 20 symbols.
the formula for this is: n! as a numerator and n1!, n2!,....nk.
n= all summations of all of the symbols
ex. 4 (x+y+2+a+b) to the 20th power coeffecient 20
x5 power plus y7 power, plus z8 power=20
a numerator of 20! 20-19 with a demonator of 5!7!8!10!0!-5,-2 then cancel.
ex.4 continued
(a+b+c+d)8 a3b1c2d2=8 8! with a denominator of 3!1!2!2!= a numerator of
8times 7times 6 times 5 times 4 times 3 with a denominator of
3!1!2!2!= 3 times 2 times 2 times 2=
56 times 30= 1680
this is from the class notes of 2/21/09 and on page 688 of the book. Know this information for the test.
that is all for now.
I can and will do good. I will pass this test and the class. The power of positive thinking. I will do it, and I can do it.
Marie Zajac CPC
ex. 2
How many intergers between 1000, and 9999 divisible by 5 has 4 digits.
10 digits from 10-100.
9,10,10,2, only choose from 0-5 or two choices.
9 is 1-9, 10 is 0-9 choices,
the product rule is 9 times 10 times 10 times 10, times 2 = 1800
2. second rule: formula: factorial
0!=1
n!=1 times 2-n
1!=1
2!=1 times 2 =2
3!=1 times 2 times 3=6
4!=1 times 2 times 3 times 4 = 24
3rd rule: Factorial rule and the product rule:
example 3.
3 places or 3 boxes =
3 times 2 times 1 = 6
3 places to put people.
Arrangements of n distinct objects page 688
n=n1,+ n2, + .....nk
ex. 20 cards some cards may have 20 letters.
5 A
6 B
3 C
6 D
how many different ways to arrange the 20 symbols.
the formula for this is: n! as a numerator and n1!, n2!,....nk.
n= all summations of all of the symbols
ex. 4 (x+y+2+a+b) to the 20th power coeffecient 20
x5 power plus y7 power, plus z8 power=20
a numerator of 20! 20-19 with a demonator of 5!7!8!10!0!-5,-2 then cancel.
ex.4 continued
(a+b+c+d)8 a3b1c2d2=8 8! with a denominator of 3!1!2!2!= a numerator of
8times 7times 6 times 5 times 4 times 3 with a denominator of
3!1!2!2!= 3 times 2 times 2 times 2=
56 times 30= 1680
this is from the class notes of 2/21/09 and on page 688 of the book. Know this information for the test.
that is all for now.
I can and will do good. I will pass this test and the class. The power of positive thinking. I will do it, and I can do it.
Marie Zajac CPC
Saturday, February 21, 2009
Mathematical Concepts 115 ch. 11
Chapter 11: 2/21/09 notes in class and from the text.
Discusses differant counting methods:
1. The tree diagram; page 674.
The tree diagram is a method of building numbers from a set of digits.
Foe example; A,B,C,
can be diagramed as many possible combinations availabe;
ABC, ACB, BAC, BCA, CAB, CBA,
The total number of combinations are 6.
2. The product Rule: with uniformity criterion, and the Fundamental counting principle;
ex.1. This is a multiple part task involving all parts to be the same with the same number of choices no matter what the previous choices were in the past. The formula is: n1,times n2,.....nk
another example is to have 5 choices for an I.D. card and what are all of the possibilities: = A,B,C,D, 1,2,3,
ADCC, 322 becomes the answer.
there are 4 possibilities: n1 is 4 n2 is 4 n3 is4 n4is 3 n5is 3. There are 4 possibilities, that is why n1-n3 is a 4. n-4-5 is a 3; because of the three possiblities. The product rule or the fundamental counting principle:
is n4 4.4.4.3.3 The answer is then given by the product.
That is all for now. I will continue later.
Marie Zajac with on a journey towards a bachelor's degree in psychology. I will do it.
Discusses differant counting methods:
1. The tree diagram; page 674.
The tree diagram is a method of building numbers from a set of digits.
Foe example; A,B,C,
can be diagramed as many possible combinations availabe;
ABC, ACB, BAC, BCA, CAB, CBA,
The total number of combinations are 6.
2. The product Rule: with uniformity criterion, and the Fundamental counting principle;
ex.1. This is a multiple part task involving all parts to be the same with the same number of choices no matter what the previous choices were in the past. The formula is: n1,times n2,.....nk
another example is to have 5 choices for an I.D. card and what are all of the possibilities: = A,B,C,D, 1,2,3,
ADCC, 322 becomes the answer.
there are 4 possibilities: n1 is 4 n2 is 4 n3 is4 n4is 3 n5is 3. There are 4 possibilities, that is why n1-n3 is a 4. n-4-5 is a 3; because of the three possiblities. The product rule or the fundamental counting principle:
is n4 4.4.4.3.3 The answer is then given by the product.
That is all for now. I will continue later.
Marie Zajac with on a journey towards a bachelor's degree in psychology. I will do it.
Monday, September 22, 2008
Counseling
Open ended questins can focus on meaning.
Summarizing: Are sentences to place everything together at the end of a counseling session. Summarizing is not paraphasing, or reflecting. A summary ties everything together.
1. Content
2. major feelings
3. meaning issues and themes,
4. future plans.
Focused Summary: Is a tool to assist with a focus on the major themes or issues that the client has identified. A focus summary helps a client to be on track.
Signal summary: Is a signal from the counselor that says we can move on to a different topic now. Before we move on lets summarize first, then we can continue again with something else of interest to you.
Thematic Summaries: Is an advanced reflecting skill. The counselor is able to make connections between content, meaning, emotions, expressed by the client in many ways. It provides new information to the client. This summary pushes the client to an even deeper level of awareness.
Planning Summaries: Is a review of the progress that the client has made. A discussion on all of the agreed upon issues, and a wa to bring closure to the session.
The non-judgemental listening cycle: is a sequencial cycle to follow as each topic is discussed by the client.
1. Open questions,
2. Minimal encouragers; Okay, uh uh, yes, go on, Tell me more,
3. closed questions important facts.
4. Paraphrase
5. Reflection of feeling
6. reflection of meaning,
7. Summary
The questioning cycle found in early training;
1. Open question
2. Minimal encourager
3. Door opener
4. Closed question
5. Paraphrase
6. Closed questione
7. Closed question.
Begining helpers can avoid giving advice by only stating the last word stated from the client.
6.
Summarizing: Are sentences to place everything together at the end of a counseling session. Summarizing is not paraphasing, or reflecting. A summary ties everything together.
1. Content
2. major feelings
3. meaning issues and themes,
4. future plans.
Focused Summary: Is a tool to assist with a focus on the major themes or issues that the client has identified. A focus summary helps a client to be on track.
Signal summary: Is a signal from the counselor that says we can move on to a different topic now. Before we move on lets summarize first, then we can continue again with something else of interest to you.
Thematic Summaries: Is an advanced reflecting skill. The counselor is able to make connections between content, meaning, emotions, expressed by the client in many ways. It provides new information to the client. This summary pushes the client to an even deeper level of awareness.
Planning Summaries: Is a review of the progress that the client has made. A discussion on all of the agreed upon issues, and a wa to bring closure to the session.
The non-judgemental listening cycle: is a sequencial cycle to follow as each topic is discussed by the client.
1. Open questions,
2. Minimal encouragers; Okay, uh uh, yes, go on, Tell me more,
3. closed questions important facts.
4. Paraphrase
5. Reflection of feeling
6. reflection of meaning,
7. Summary
The questioning cycle found in early training;
1. Open question
2. Minimal encourager
3. Door opener
4. Closed question
5. Paraphrase
6. Closed questione
7. Closed question.
Begining helpers can avoid giving advice by only stating the last word stated from the client.
6.
Counseling
World view refers to a person's view of self, others, and the world around them.
1. View of self. I am a good person, I am a selfish person, I am licky, etc.
2. View of others. Men are all alike, People are (unrealistic) kind etc.
3. Values: Conflict is bad. Men should be the head of the family, etc.
4. Beliefs about the world in general. life is a jungle. Life is a vale of tears etc.
1. View of self. I am a good person, I am a selfish person, I am licky, etc.
2. View of others. Men are all alike, People are (unrealistic) kind etc.
3. Values: Conflict is bad. Men should be the head of the family, etc.
4. Beliefs about the world in general. life is a jungle. Life is a vale of tears etc.
Counseling
The inner-circle strategy:
The inner circle strategy involves identifying a diagram labeled from a to e. A is the inner most circle to e as the outer most part of the circle. The e circle is the most public information. At the inner most circle; are the very private personal issues such as, anger problems, resentments towards other people , negative views of the self, and secrets that could be considered immoral or dishonest, would ass be at the level of a. The rings b,c, and d are secrets areas that are increasing in levels of secrecy.
A helper could have a client to identify different areas in the diagram. The client could then name people who have acces the these areas on the diagram. This could be a tool for a helper assist a client to move forwards from superficial to be able to discuss deeper issues, and a better self awareness.
The inner circle strategy involves identifying a diagram labeled from a to e. A is the inner most circle to e as the outer most part of the circle. The e circle is the most public information. At the inner most circle; are the very private personal issues such as, anger problems, resentments towards other people , negative views of the self, and secrets that could be considered immoral or dishonest, would ass be at the level of a. The rings b,c, and d are secrets areas that are increasing in levels of secrecy.
A helper could have a client to identify different areas in the diagram. The client could then name people who have acces the these areas on the diagram. This could be a tool for a helper assist a client to move forwards from superficial to be able to discuss deeper issues, and a better self awareness.
Counseling
I am studying for a test. The test covers chapters 8 and 9. Chapter 8 is entitled: Reflecting skills: Reflecting Meaning and Summarizing:
Constructivism: every person actively with their expeeriences, and based on their language and belief system, they construct reality along with in accordance towards others. Every person has their own way at looking at the world. Helpers are to unlayer all of the underlying meanings of the clients messages.
Meaning uncovering the next layer:
Understanding the content of the story.
Meanings are a series of generalizations to assist an individual to navigate throughout life. A collection of a persons worldview. Reflection of meaning can become a self awareness of perspective. What perspectives does a client have of his/her meaning of life experiences. Beliefs and values could be taken inteo account as well. Underlying feelings will be discussed as well with reflection.
Depth of the clients responses are based upon the counselor's reflection skills. Three depeth levels are included:
1. level 1, What happened? Content. Level one corresponds with Paraphrasing. Paraphraing involves the cognitive tehinking level.
2. Level 2, Feelings. How did you feel? level 2 involves a reflection of feelings a client is having.
3. Level 3, Is a reflection on meaning. What did it mean. Also, at the third level underlying meanings of perceptions are identified.
Reflecting meaning to a client can assist the client with an awareness of perspectives. A goal can also be identified easier at level 3. Perspective shifts can also be accomplished. A reflection on feelings and meanings a client can go deeper into a sense of self awareness.
Challenging the client to go deeper: The inner circle strategy.
Arnold Lazarus: Founder of the inner circle strategy.
Constructivism: every person actively with their expeeriences, and based on their language and belief system, they construct reality along with in accordance towards others. Every person has their own way at looking at the world. Helpers are to unlayer all of the underlying meanings of the clients messages.
Meaning uncovering the next layer:
Understanding the content of the story.
Meanings are a series of generalizations to assist an individual to navigate throughout life. A collection of a persons worldview. Reflection of meaning can become a self awareness of perspective. What perspectives does a client have of his/her meaning of life experiences. Beliefs and values could be taken inteo account as well. Underlying feelings will be discussed as well with reflection.
Depth of the clients responses are based upon the counselor's reflection skills. Three depeth levels are included:
1. level 1, What happened? Content. Level one corresponds with Paraphrasing. Paraphraing involves the cognitive tehinking level.
2. Level 2, Feelings. How did you feel? level 2 involves a reflection of feelings a client is having.
3. Level 3, Is a reflection on meaning. What did it mean. Also, at the third level underlying meanings of perceptions are identified.
Reflecting meaning to a client can assist the client with an awareness of perspectives. A goal can also be identified easier at level 3. Perspective shifts can also be accomplished. A reflection on feelings and meanings a client can go deeper into a sense of self awareness.
Challenging the client to go deeper: The inner circle strategy.
Arnold Lazarus: Founder of the inner circle strategy.
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