Worksheet: Using Permutations to Find Probability

In this worksheet, we will practice finding the probability of an event by calculating the number of outcomes using permutation.

Q1:

Ethan, Jacob, 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 Jacob arriving first and Ethan arriving second.

  • A125
  • B15
  • C25
  • D115
  • E120

Q2:

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

  • A112
  • B172
  • C5252
  • D10729
  • E542

Q3:

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

  • A1602
  • B1180,901
  • C0
  • D1361,802
  • E0.5

Q4:

Matthew 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.

  • A15
  • B190
  • C150
  • D1100

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?

  • A0
  • B16
  • C14
  • D12
  • E34

Q6:

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

  • A120,160
  • B128
  • C18
  • D156
  • E140,320

Q7:

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

  • A12,450
  • B1325
  • C25
  • D0
  • E150

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”.

  • A1831,600
  • B111
  • C169,300
  • D311
  • E134,650

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”.

  • A160
  • B16
  • C120
  • D15
  • E1120

Q10:

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

  • A1302,400
  • B1252
  • C110
  • D130,240
  • E13,628,800

Q11:

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

  • A1151,200
  • B1120
  • C110
  • D1604,800
  • E13,628,800

Q12:

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

  • A190,720
  • B1126
  • C19
  • D13,024
  • E1362,880

Q13:

In how many ways can the letters of the word LION be arranged?

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.