Counting/Probability Quiz

A male student is picking out a tuxedo for prom. At the store, he can choose between 3 different tuxedos, 4 different vests, and 2 different pairs of shoes. Which of the following represents the correct calculation of the number of different outfits he can create if he selects one item from each category?

• 3 x 2 x 1 x 4 x 3 x 2 x 1 x 2 x 1

• 3 x 4 x 2

• 3 + 2 + 1 + 4 + 3 + 2 + 1 + 2 + 1

• 3 + 4 + 2

You are on a game show trying to guess the price of a car by filling in 5 squares with single digit numbers. You know that the first digit has to be a 1 or a 2, the last digit is a 9, and that there is no repetition of digits. Which of the following represents the correct calculation of the number of different ways that you can fill in the squares?

• 2 x 10 x 10 x 10 x 1

• 2 x 9 x 8 x 7 x 1

• 2 x 8 x 7 x 6 x 1

• 2 x 8 x 8 x 8 x 1

Which of the following represents the correct calculation of the number of different seven - digit phone numbers (### - ####) can be formed if the first digit cannot be a 0 or a 1?

• 7 x 9 x 9 x 9 x 9 x 9 x 9

• 8 x 10 x 10 x 10 x 10 x 10 x 10

• 8 x 9 x 8 x 7 x 6 x 5 x 4

• 7 x 8 x 7 x 6 x 5 x 4 x 3

Which of the following represents the correct calculation of the number of ways that 4 women and 2 men can line up in a line if there are no restrictions on how the people line up?

• 4 x 2

• 4 x 3 x 2 x 1 x 2 x 1

• 6 x 5 x 4 x 3 x 2 x 1

• 4 x 4 x 4 x 4 x 2 x 2

Which of the following represents the correct calculation of the number of ways that 4 women and 2 men can line up in a line if the women must all get in line before the men?

• 4 x 2

• 4 x 3 x 2 x 1 x 2 x 1

• 6 x 5 x 4 x 3 x 2 x 1

• 4 x 4 x 4 x 4 x 2 x 2

Which of the following represents the correct calculation of the number of ways that a principal can choose 10 students to be on prom committee if there are 30 students in the grade who would like to be on the committee?

• ₃₀P₁₀

• ₃₀C₁₀

• ₁₀P₃₀

• ₁₀C₃₀

How many ways can a principal choose 4 students from a 10 person prom committee to be the president, vice – president, treasurer, and secretary?

• ₁₀P₄

• ₁₀C₄

• ₄P₁₀

• ₄C₁₀

Which of the following represents the correct calculation of the number of distinguishable permutations of the letters of the word UNDERSTANDING?

• 13!

• 13!/(3!2!)

• 13!/3!

• 13!/(2!2!)

CHOOSE THE CORRECT METHOD FOR CALCULATING THE PROBABILITY OF DRAWING THE INDICATED CARDS CONSECUTIVELY FROM A STANDARD 52 – CARD DECK OF CARDS IF EACH CARD THAT IS DRAWN IS NOT RETURNED TO THE DECK AFTER IT IS DRAWN.

A black card is drawn, and then a heart is drawn

• (26/52) x (13/52)

• (26/52) + (13/52)

• (26/52) x (13/51)

• (26/52) + (13/51)

CHOOSE THE CORRECT METHOD FOR CALCULATING THE PROBABILITY OF DRAWING THE INDICATED CARDS CONSECUTIVELY FROM A STANDARD 52 – CARD DECK OF CARDS IF EACH CARD THAT IS DRAWN IS NOT RETURNED TO THE DECK AFTER IT IS DRAWN.

An ace is drawn, then a king is drawn, then another ace is drawn

• (4/52) x (4/52) x (3/52)

• (4/52) x (4/51) x (4/50)

• (4/52) x (4/51) x (3/50)

• (4/52) + (4/51) + (3/50)