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Worksheet: Using Permutations to Count Outcomes

Q1:

David and Amelia are graduating in a class of 57 students. If each student is assigned a number from 1 to 57 at random, what is the probability that David’s number will be 1 and Amelia’s will be 2?

  • A 5 5 5 7
  • B 2 5 7
  • C 1 3 2 4 9
  • D 1 3 1 9 2
  • E 3 1 9 1 3 1 9 2

Q2:

Anthony and Sophia are graduating in a class of 45 students. If each student is assigned a number from 1 to 45 at random, what is the probability that Anthony’s number will be 1 and Sophia’s will be 2?

  • A 4 3 4 5
  • B 2 4 5
  • C 1 2 0 2 5
  • D 1 1 9 8 0
  • E 1 9 7 9 1 9 8 0

Q3:

In how many ways can you order four people sitting on a bench?

Q4:

In how many ways can 2 people sit on 8 chairs?

Q5:

In how many ways can 4 people sit on 9 chairs?

Q6:

How many different 4-digit numbers can be formed from the digits 5, 3, 2, 7, and 6? Assume no number can be used more than once.

Q7:

In how many different ways can 8 friends sit in a line if 2 of them, Isabella and Scarlett, must sit next to each other?

Q8:

In how many different ways can 9 friends sit in a line if 2 of them, Elizabeth and Hannah, must sit next to each other?