Permutations and Combinations with Probability

Determine whether the following scenarios are a permutation or a combination:
 
Selecting a lead and an understudy for a school play.

• Combination

• Permutation

Find the number of possibilities:
A group of 25 people are going to run a race.  The top 8 finishers advance to finals.

• 625

• 4.36 X 10¹⁰

• 1,081,575

Rob and Mary are planning trips to 9 countries this year.  There are 13 countries they would like to visit.  They are deciding which countries to skip.

• combination

• permutation

• neither

Find the number of words, with or without meaning, that can be formed with the letters of the word ‘CHAIR’.

• 5

• 3125

• 120

• 25

What does ₁₀P₅ mean?

• Permutations with 5 choices and 10 positions

• Permutations with 10 choices and 5 positions

• Permutations with 5 numbers and 10 operations

• Permutations with 5 hot dogs and 10 drinks

Rylan’s basketball team has 11 players. How many ways can his coach choose five starting players? Positions do not matter

• 462

• 55440

• 55

• 1000

There are 68 juniors at the high school. How many ways can they elect a president, vice president, and secretary?

• 300696

• 317750

• 375

• 1953125

Ashlyn needs to bring a dessert to her dinner party. If the bakery has eight pies to choose from, how many ways can Ashlyn choose three?

• 336

• 56

• 24

• 100

If Lucas owns 11 hoodies, how many ways can he choose four to bring on vacation?

• 44

• 7920

• 330

• 121

A disc jockey has to choose three songs for the last few minutes of his evening show.  If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?

• 84

• 504

• 9!

• 3!