# Lesson Worksheet: Using Permutations to Find Probability Mathematics • 12th Grade

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.

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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.

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Q3:

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.

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Q4:

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

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Q5:

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?

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Q6:

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”.

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Q7:

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”.

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Q8:

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

Q9:

Osama and Bandar are twins in a class of 17 students. 17 chairs are placed in a line for an assembly and the students are randomly assigned a seat. What is the probability of the twins sitting in the first two seats?

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Q10:

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?

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