Factorial and Permutations Word Problems

Determine whether the question would be a permutation or combination: Five students from 90 will be selected to count ballots for the Class President election. How many groups of 5 students could be selected to count ballots?

(a)  

• Combination

• Permutation

• Neither

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!

Decide whether you'd solve using a Permutation, Combination, or simply need a single factorial, then match the cards accordingly.

• Ribbons are being awarded for 1st through 5th place to the top 5 dogs in a dog show.

• Combination

• A lock has a code of 3 numbers between 1 and 15. How many codes can be created if no numbers repeat

• Factorial

• The principal would like to assemble a committee of 8 students from the 12-member student council.

• 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

Find the number of possibilities:
A team of 17 softball players needs to choose three players to refill the water cooler.

• 272

• 4080

• 680

How many ways can a stylist arrange 5 of 8 vases from left to right in a store display?

• 672

• 40

• 6720

Determine whether the following scenarios are a permutation or a combination:

Selecting a lead and an understudy for a school play.
(a)  

• Permutation

• Combination

In how many ways can 6 people arrange themselves in a row for picture taking?

• 24

• 60

• 120

• 720

How many numbers of permutations can be drawn using 7 keys around a key ring?

• 60

• 120

• 240

• 720

What is the value of 5!?

• 25

• 15

• 120

• 720