Worksheet: Using Permutations to Find Probability

In this worksheet, we will practice finding probabilities using permutations.

Q1:

Sherif, Bassem, and three of their coworkers each take the bus to work. If they each have an equal chance of arriving first, determine the probability of Bassem arriving first and Sherif arriving second.

  • A
  • B
  • C
  • D
  • E

Q2:

A small combination padlock can be opened by entering three different specified numbers from 1 to 9 in a specified order. Maged has 10 attempts to guess the combination. Determine the probability of him opening the lock.

  • A
  • B
  • C
  • D
  • E

Q3:

Two people are chosen randomly from a group of six hundred two. What is the probability that Maged was selected first and Sherif second?

  • A
  • B
  • C0
  • D
  • E0.5

Q4:

Sameh received 10 letters in the mail. If he can read them in any order, determine the probability that he reads the letter from his parents and then that from his grandmother before the others.

  • A
  • B
  • C
  • D

Q5:

A number is formed at random using 2 distinct digits from the set { 2 , 5 , 8 , 9 } . What is the probability that both the digits are odd?

  • A 1 2
  • B 1 4
  • C 3 4
  • D 1 6
  • E 0

Q6:

If you randomly select a permutation of the letters shown, what is the probability that they spell KINETICS?

  • A 1 5 6
  • B 1 4 0 3 2 0
  • C 1 2 8
  • D 1 2 0 1 6 0
  • E 1 8

Q7:

Nader and Fares each bought one raffle ticket. If 50 tickets were randomly sold, what is the probability that Nader got ticket number 20 and Fares got ticket number 26?

  • A
  • B
  • C0
  • D
  • E

Q8:

The letters I, I, I, I, P, P, S, S, S, S, and M are placed in a bag. Determine the probability of randomly selecting letters from the bag in an order that spells the word “MISSISSIPPI”.

  • A 1 6 9 3 0 0
  • B 1 8 3 1 6 0 0
  • C 1 1 1
  • D 1 3 4 6 5 0
  • E 3 1 1

Q9:

The letters E, R, R, R, and O are placed in a bag. Determine the probability of randomly selecting letters from the bag in an order that spells the word “ERROR”.

  • A 1 6
  • B 1 1 2 0
  • C 1 6 0
  • D 1 2 0
  • E 1 5

Q10:

If you randomly select a permutation of the letters shown, what is the probability that they spell ATTRACTIVE?

  • A 1 3 0 2 4 0
  • B 1 3 6 2 8 8 0 0
  • C 1 2 5 2
  • D 1 3 0 2 4 0 0
  • E 1 1 0

Q11:

If you randomly select a permutation of the letters shown, what is the probability that they spell CONVINCING?

  • A 1 6 0 4 8 0 0
  • B 1 3 6 2 8 8 0 0
  • C 1 1 2 0
  • D 1 1 5 1 2 0 0
  • E 1 1 0

Q12:

If you randomly select a permutation of the letters shown, what is the probability that they spell FANTASTIC?

  • A 1 3 0 2 4
  • B 1 3 6 2 8 8 0
  • C 1 1 2 6
  • D 1 9 0 7 2 0
  • E 1 9

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