Question 1

Which of the following scenarios requires the use of a permutation rather than a combination?

Accepted Answer

Assigning 1st, 2nd, and 3rd place medals to 10 runners in a race.

Question 2

Evaluate $$6P2$$ using the permutation formula.

Accepted Answer

$$30$$

Question 3

How many different ways can the letters in the word 'SEEM' be arranged?

Accepted Answer

$$24$$

Question 4

A jury of 12 people is chosen from a pool of 35 potential jurors. Which formula should be used to determine the number of possible juries?

Accepted Answer

$$\displaystyle \frac{35!}{12!\,23!}$$

Question 5

How many different ways can a chairperson and an assistant chairperson be selected from 7 scientists?

Accepted Answer

$$42$$

Question 6

Evaluate $$\displaystyle \frac{6!}{4!}.$$

Accepted Answer

$$30$$

Question 7

How many different ways can Ms. Temple arrange 4 of her 6 new students in a row?

Accepted Answer

$$360$$

Question 8

Which of the following is the correct formula for the number of combinations of $$n$$ items taken $$r at a $$time?

Accepted Answer

$$\displaystyle \frac{n!}{r!(n-r)!}$$

Question 9

A service club has 8 freshmen. How many different ways can 5 of them be chosen for a cleanup crew?

Accepted Answer

$$56$$

Question 10

How many different arrangements are possible for the letters in the word 'MISSISSIPPI'?

Accepted Answer

$$34650$$

Question 11

Suppose you randomly select 3 pool balls from a set numbered 1 to 15. What is the probability that you select balls numbered 5, 7, and 9?

Accepted Answer

$$\displaystyle \frac{1}{455}$$

Question 12

How many different ways can Kayla arrange 4 of her 9 favorite photos on a shelf?

Accepted Answer

$$3024$$

Question 13

Which of the following is true about permutations and combinations?

Accepted Answer

Permutations are used when order is important.

Question 14

How many different ways can you arrange 3 yellow books, 5 blue books, 2 red books, and 1 green book on a shelf?

Accepted Answer

$$27,720$$

Question 15

A college student is choosing 3 classes to take during her first, second, and third semester from 5 elective classes. How many possible ways can she schedule the three classes?

Accepted Answer

$$60$$

Permutations and Combinations: Structured Study Notes for Introductory Statistics

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