Permutations and Combinations

There are 5 doors to a lecture room. In how many ways can a student enter the room through a door and leave the room by a different door?

• 10

• 9

• 20

• 625

• 1024

In how many ways can 3 students be selected from a group of 12 students to represent a school in the inter school essay competition

• 3

• 12!

• 1320

• 220

• 36

How many words can be formed by re-arranging the letters of the word PROBLEMS such that P and S occupy the first and last position respectively? (Note: The words thus formed need not be meaningful)

• 8/2

• 8! - 2!

• 6!

• 8! - 2! * 7!

• 6! * 2!

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!

How many 2-digit numbers can you make using the digits 1, 2, 3, & 4 without repeating the digits?

• 90
• 100
• 12
• 24

Eva has eight glasses of water.  In how many different orders can the glasses of water be arranged?

• 8
• 64
• 8!
• 56

How would you solve?
A book club offers a choice of 8 books from a list of 40.  In how many ways can a member make a collection?

• Permutation
• Combination
• Factorial
• MPC

How would you solve?
From the 20 DVD's you purchased this past year, you plan to take five with you on vacation.  How many different sets of five DVD's can you take?

• Permutation
• Combination
• Factorial
• MPC

The ski club with ten members is to choose three officers for captain, co-captain and secretary.  How many ways can those offices be filled?

• 720
• 120
• 10!

Rylan’s basketball team has 11 players. How many ways can his coach choose five starting players?

• 462
• 55440
• 55
• 1000