Q: A four-digit code is formed using the digits 0-9, with no digit repeated. How many such codes are possible?

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

Q: A student advisory board has 17 members. What is the probability that three specific members are randomly chosen to serve as chair, secretary, and webmaster (one for each position)?

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

Q: A food manufacturer analyzes 400 corn kernels, 3 of which are toxic. If 4 kernels are selected at random, what is the probability that exactly one is toxic?

$$\dfrac{3C1 \times 397C3}{400C4}$$

Q: A warehouse employs 24 first-shift and 17 second-shift workers. If 8 workers are chosen at random, what is the probability that 6 are first-shift workers?

$$\dfrac{24C6 \times 17C2}{41C8}$$

Q: You look over the songs on a jukebox and like 15 of the 56 songs. What is the probability that you like the next three songs played (no repeats)?

$$\dfrac{15}{56} \times \dfrac{14}{55} \times \dfrac{13}{54}$$

Question 1

Which of the following best describes a permutation?

Accepted Answer

An arrangement of objects where order matters.

Question 2

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

Accepted Answer

$$9!$$

Question 3

A four-digit code is formed using the digits 0-9, with no digit repeated. How many such codes are possible?

Accepted Answer

$$10 	imes 9 	imes 8 	imes 7$$

Question 4

A race has 43 cars. In how many ways can the first, second, and third place be awarded?

Accepted Answer

$$43 	imes 42 	imes 41$$

Question 5

A subdivision 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

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

Question 6

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

Accepted Answer

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

Question 7

A student advisory board has 17 members. What is the probability that three specific members are randomly chosen to serve as chair, secretary, and webmaster (one for each position)?

Accepted Answer

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

Question 8

How many distinguishable ways can the letters in the word 'MISSISSIPPI' be arranged?

Accepted Answer

$$\dfrac{11!}{1!4!4!2!}$$

Question 9

A food manufacturer analyzes 400 corn kernels, 3 of which are toxic. If 4 kernels are selected at random, what is the probability that exactly one is toxic?

Accepted Answer

$$\dfrac{3C1 	imes 397C3}{400C4}$$

Question 10

An environmental agency analyzes 50 farms, 8 of which are contaminated. If 10 farms are selected, how many ways can 2 contaminated and 8 noncontaminated farms be chosen?

Accepted Answer

$$8C2 	imes 42C8$$

Question 11

A warehouse employs 24 first-shift and 17 second-shift workers. If 8 workers are chosen at random, what is the probability that 6 are first-shift workers?

Accepted Answer

$$\dfrac{24C6 	imes 17C2}{41C8}$$

Question 12

You choose 4 people at random from a group of 1200. If 7% of people rate their financial shape as 'Excellent', what is the probability all four chosen rate themselves as 'Excellent'?

Accepted Answer

$$(0.07)^4$$

Question 13

You look over the songs on a jukebox and like 15 of the 56 songs. What is the probability that you like the next three songs played (no repeats)?

Accepted Answer

$$\dfrac{15}{56} 	imes \dfrac{14}{55} 	imes \dfrac{13}{54}$$

Question 14

The offices of president, vice president, secretary, and treasurer for a club will be filled from 14 candidates, 6 of whom are on the debate team. What is the probability all offices are filled by debate team members?

Accepted Answer

$$\dfrac{6P4}{14P4}$$

Question 15

Which formula would you use to count the number of ways to arrange all the letters in the word 'BALLOON'?

Accepted Answer

$$\dfrac{7!}{2!2!}$$

Question 16

Which counting technique should be used to determine the number of ways to assign 5 different prizes to 5 people?

Accepted Answer

Permutation: $$5!$$

Introductory Statistics: Probability and Counting Techniques Study Guide

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