Q: How many four-digit codes can be formed from the digits 0-9 if no digit is repeated?

$$10 \times 9 \times 8 \times 7$$

Q: A student advisory board has 17 members. Three members are randomly chosen to serve as chair, secretary, and webmaster. What is the probability that a specific group of three students is chosen for these positions?

$$\frac{1}{17 \times 16 \times 15}$$

Question 1

Which of the following best describes a permutation?

Accepted Answer

An ordered arrangement of objects.

Question 2

How many different ways can the first row of a blank $$9 	imes 9$$ Sudoku grid be filled, using each digit 1 to 9 exactly once?

Accepted Answer

$$9!$$

Question 3

What is the formula for the number of permutations of $$n$$ distinct objects?

Accepted Answer

$$n!$$

Question 4

A race has 33 cars. In how many ways can the cars finish first, second, and third?

Accepted Answer

$$33 	imes 32 	imes 31$$

Question 5

Which formula gives the number of permutations of $$n$$ objects taken $$r at a $$time?

Accepted Answer

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

Question 6

How many four-digit codes can be formed from the digits 0-9 if no digit is repeated?

Accepted Answer

$$10 	imes 9 	imes 8 	imes 7$$

Question 7

A building contractor has 6 one-story, 4 two-story, and 2 split-level houses. In how many distinguishable ways can the 12 houses be arranged?

Accepted Answer

$$\frac{12!}{6!4!2!}$$

Question 8

Which formula is used to find the number of combinations of $$n$$ objects taken $$r at a $$time?

Accepted Answer

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

Question 9

A state receives 16 bids for a project and will hire 4 companies. How many different groups of 4 companies can be selected?

Accepted Answer

$$\frac{16!}{12!4!}$$

Question 10

Which principle states that if one event can occur in $$m$$ ways and a second event in $$n$$ ways, the two events can occur in $$m 	imes n$$ ways?

Accepted Answer

Fundamental Counting Principle

Question 11

A student advisory board has 17 members. Three members are randomly chosen to serve as chair, secretary, and webmaster. What is the probability that a specific group of three students is chosen for these positions?

Accepted Answer

$$\frac{1}{17 	imes 16 	imes 15}$$

Question 12

What is the probability of being dealt 5 diamonds from a standard deck of 52 playing cards?

Accepted Answer

$$\frac{\binom{13}{5}}{\binom{52}{5}}$$

Question 13

Which of the following situations requires the use of combinations rather than permutations?

Accepted Answer

Selecting a committee of 4 people from a group of 10.

Question 14

If you have 8 different books and want to arrange 5 of them on a shelf, how many different arrangements are possible?

Accepted Answer

$$\frac{8!}{3!}$$

Question 15

Which of the following is NOT a property of permutations?

Accepted Answer

Order does not matter.

Counting Principles and Permutations in Probability

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