Worksheet: Finding Probability Using Permutations

The calculation of probabilities often involves counting the number of outcomes of various events. In this worksheet, we will learn how to find probability using permutations.

Q1:

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.

Q2:

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

A
B
C0
D
E0.5

Q3:

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?

Q4:

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?

Q5:

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.

Q6:

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.

Q7:

A number is formed at random using 2 distinct digits from the set . What is the probability that both the digits are odd?

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”.

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”.

Q10:

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

Q11:

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

Q12:

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

Q13:

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