Additional Topics in Probability and Counting

Your friends rented 6 different video games.

In how many different orders can you play the 6 games?

• 720 different orders

• 120 different orders

• 36 different orders

• 46646 different orders

• 6 different orders

How many ways can you draw 5 names from the jar?

• ₁₅P₅ = 360360

• ₁₅C₅ = 3003

• 12! = 479001600

• 15 ⋅ 5 = 75

A batch of 350 raffle tickets contains four winning tickets.

You buy four tickets.

0.954873 is the approximate probability that you have:

• no winning tickets

• all of the winning tickets

• at least one winning ticket

• at least one non-winning ticket

• only one winning ticket

A corporation has six male senior executives and four female senior executives.

Four senior executives are chosen at random to attend a technology seminar.

Find the approximate probability of choosing:

• 0.004762

• four women

• 0.428571

• two men and two women

• 0.071429

• four men

• 0.114286

• one man and three women

There are 18 people running in a cross country race. How many possible ways are there to place the runners in first, second, and third?

• ₁₈P₃ = 4896

• ₁₈C₃ = 816

• 15! = 1307674368000

• 6! = 720

A lock has four dials. On each dial are the digits 0 to 9.

How many possible combinations are there if you cannot reuse a number?

• 40

• 5040

• 6561

• 10,000

How many different sets of 4 games could you choose to rent?

• ₂₀P₄ = 116280

• ₂₀C₄ = 4845

• 16! = 20922789888000

The Smith Family has a garage door that opens with a 4-digit PIN. They decide to base the code on the birthday of 01/24/36. How many PINs are there that use four of the digits in the birthday?

• ₆P₄ = 360

• ₆C₄ = 15

• 6 ⋅ 4 = 24

There are 6 class periods in the school day. There are 10 subjects to choose from. How many different class schedules are possible?

• ₁₀P₆ = 151200

• ₁₀C₆ = 210

• 4! = 24

• 6 ⋅ 10 = 60

There are 30 songs on your music player. In how many different ways can you arrange 20 songs to listen to while exercising?

• ₃₀P₂₀ = 73096577329197271449600000

• ₃₀C₂₀ = 30045015

• 10! = 3628800

• 30 ⋅ 20 = 600