3.4 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

There are 20 games to choose from at the local game store.

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 15 slips of paper in each jar.

Each slip has a different name on it.

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

• ₁₅P₅ = 360360

• ₁₅C₅ = 3003

• 12! = 479001600

• 15 ⋅ 5 = 75

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

The football team will select 5 captains from their seniors.

There are 15 seniors on the team.

How many different groups of captains could be selected?

• ₁₅P₅ = 360360

• ₁₅C₅ = 3003

• 3! = 6

• 15 ⋅ 5 = 75

There are 8 finalists in the spelling bee.

The order of the contestants will be determined by a random draw.

How many different orders are possible for the final spelling bee?

• 40320

• 1

• 8

• 28

• 56

A restaurant's menu offers 8 different sandwiches and 5 side dishes. How many lunch menu combinations can you order?

• ₈P₅ = 6720

• ₈C₅ = 56

• 3! = 6

• 8 ⋅ 5 = 40

A full house consists of three of one kind and two of another kind.

Set up the calculation to find the probability of being dealt a full house consisting of three kings and two queens.

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