# M166 Ch 6 – Permutation and Combination (6.3, 6.4) Factorial :

```M166
Ch 6 – Permutation and Combination (6.3, 6.4)
TAMU – Spring 2014
Calculator Functions:
1. Factorial :
MATH → scroll to PRB → scroll to 4 : ! → ENTER
Example: Find 5! .
Enter 5 → MATH → scroll to PRB → scroll to 4 : ! → ENTER
2. Permutation : nPr
Enter n → MATH → scroll to PRB → scroll to 2 : nPr → Enter r → ENTER
Example: Find P(5 , 2) .
Here, n = 5 and r = 2.
Enter 5 → MATH → scroll to PRB → scroll to 2 : nPr → Enter 2 → ENTER
3. Combination : nCr
Enter n → MATH → scroll to PRB → scroll to 3 : nCr → Enter r → ENTER
Example: Find C(5 , 2) .
Here, n = 5 and r = 2.
Enter 5 → MATH → scroll to PRB → scroll to 3 : nCr → Enter 2 → ENTER
4. Binomial Trials:
a) binompdf – Exactly k successes
2nd VARS → scroll down to A : binompdf( → Enter n → Press the Comma key → Enter p → Press
the Comma key → Enter k → ENTER
where n : Total number of trials ; p : probability of a success ; k : number of successes
b) binomcdf – at most k successes
2nd VARS → scroll down to B : binomcdf( → Enter n → Press the Comma key → Enter p → Press
the Comma key → Enter k → ENTER
Note : “binomcdf” function is also used to calculate “at least” k successes. We'll discuss in class how
that's done.
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M166
Ch 6 – Permutation and Combination (6.3, 6.4)
TAMU – Spring 2014
1. A card is picked from a standard deck of 52 cards and then a 6-sided die is rolled. How many
possible outcomes are there?
2. Kitty has 3 dolls, 4 doll- dresses, and 5 doll - shoes. How many different ways can a doll be
dressed?
3. In how many different ways can the digits in the set S = {1, 2, 3} be arranged?
4. How many ways can 10 kids be lined up to form a queue?
5. At an award ceremony, 5 couples are to be called one at a time to receive an award. In how
many ways can this be done if
a) men and women must alternate?
b) Couples are called together ?
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M166
Ch 6 – Permutation and Combination (6.3, 6.4)
TAMU – Spring 2014
6. A password can be formed with 4 letters followed by 5 digits. How many different passwords
are possible if
a) repetition of digits and/or numbers is allowed?
b) repetition of letters is not allowed?
c) repetition of digits is not allowed?
d) the first digit must be non-zero ?
7. Ted loves traveling. He wants to visit 7 cities in Great Britain, 5 in France, 3 in Germany and 4
in India. How many ways can his itinerary be made out?
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M166
Ch 6 – Permutation and Combination (6.3, 6.4)
TAMU – Spring 2014
8. 10 friends decide to take a road-trip and rent a mini van. How many seating arrangements are
possible if only 4 of them know how to drive?
9. Linda has 40 books, of which 17 are fiction, 6 are self – help, 13 are textbooks, and 4 are
cook-books. How many ways can she arrange all the books on a shelf if
a) there are no restrictions on the arrangement ?
b) books of the same category must be placed together ?
c) there's room for only 25 books ?
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M166
Ch 6 – Permutation and Combination (6.3, 6.4)
TAMU – Spring 2014
10. How many different (distinguishable) ways can we arrange the letters of the word MISSISSIPPI.
11. If there are 3 red, 5 green, and 4 blue balls, how many ways can the balls be arranged, given the
balls of same color are exactly alike?
12. Out of a total of 10 people, a committee needs to be formed with a President, a Vice-President, a
Secretary, and 3 members. How many ways can the selection be made?
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M166
Ch 6 – Permutation and Combination (6.3, 6.4)
TAMU – Spring 2014
13. An exam consists of 5 true/false questions followed by 3 multiple choice questions each with 4
answers. How many ways can a student answer all the questions if
a) he/she has to answer all the questions?
b) he/she is allowed to leave the questions blank?
14. A committee of 15 people consists of 8 men and 7 women. Find ( i ) the number if ways of
choosing a subcommittee of 5 people consisting of
a) any 5 committee members
b) all men?
c) exactly 3 men?
d) at least ?
e) at most 3 men ?
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M166
Ch 6 – Permutation and Combination (6.3, 6.4)
TAMU – Spring 2014
15. A pen holder holds 5 green, and 3 blue pens. In how many ways can you select
a) 4 pens ?
b) 4 pens, with at least 2 blue pens ?
c) 4 pens, with exactly 1 blue ?
d) 4 pens, with no blue pens ?
e) 4 pens, such that exactly 3 are of the same color ?
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M166
Ch 6 – Permutation and Combination (6.3, 6.4)
TAMU – Spring 2014
16. An unfair coin is flipped 100 times in succession. The probability of getting a heads is 1/3.
What is the probability of getting