# Lesson Worksheet: Using Combinations to Find Probability Mathematics

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

Q1:

Find the number of ways to select 3 different letters from the set .

Q2:

How many teams of four can be selected from a group of 20 people?

Q3:

A team of four is to be randomly selected from a group of ten boys and ten girls. Determine the probability that a team will contain only girls.

• A
• B
• C
• D
• E

Q4:

Thirteen boys and fifteen girls entered a draw for five free movie tickets. What is the probability that all five tickets were won by boys?

• A
• B
• C
• D
• E0

Q5:

A computer generates four-digit codes using the numbers 0–9 with no repeated digits. How many unique codes can be generated?

Q6:

Amelia invited 4 of her 24 friends over for a movie night. If she chose to invite her friends at random, what is the probability that Jennifer, Charlotte, Scarlett, and Olivia are chosen?

• A
• B
• C0
• D
• E

Q7:

Which of the following represents the number of ways of selecting 2 students out of 24 for a class activity?

• A
• B
• C
• D

Q8:

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

• A
• B
• C
• D
• E

Q9:

A bowl contains 25 marbles, each with a different color. If Benjamin selects four marbles from the bowl, what is the probability that he selects the marbles with the four colors that he wants?

• A
• B
• C
• D0
• E

Q10:

Madison wants to visit cities across the US, and she has placed the names of 32 cities into a hat. If she randomly draws 3 names from the hat, what is the probability that she gets Savannah, Austin, and Seattle?

• A0
• B
• C
• D
• E

Q11:

In how many different ways can 10 motorcycles and 9 bicycles be arranged in 2 spaces if the order is not important?

Q12:

Which of the following represents the number of ways in which the letters of the word “zebra” can be rearranged?

• A
• B
• C
• D

Q13:

Which of the following represents the number of ways in which 8 different digits can be rearranged to form an 8-digit number?

• A
• B
• C
• D

Q14:

Seven boys and eight girls entered a draw for four free movie tickets. What is the probability that all four tickets were won by boys?

• A
• B
• C
• D
• E0

Q15:

Which of the following represents the number of ways of selecting 2 students out of 17 for a class activity?

• A
• B
• C
• D

Q16:

Madison has two red cards and three blue ones. She shuffles the cards, places them face down in a row, and turns them over. What is the probability that the cards are laid out in alternate colors?

• A
• B
• C
• D1
• E

Q17:

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

• A
• B
• C
• D
• E

Q18:

Jacob has three red cards and seven blue ones. He shuffles the cards and lays them out in a line. What is the probability that at least two of the red cards are next to each other?

• A
• B
• C
• D
• E

Q19:

An ice cream stall offers eight different flavors of ice cream, and their ice cream is available in three different sizes: small, medium, and large.

How many possible combinations of flavors and sizes are there?

Assuming John chooses his ice cream completely at random, what is the probability that he chooses a small strawberry ice cream?

• A
• B
• C
• D
• E

Assuming John chooses his ice cream completely at random, what is the probability that he chooses neither chocolate nor a large ice cream?

• A
• B
• C
• D
• E

Q20:

Two distinct digits are chosen at random from the set . What is the probability that both digits are odd?

• A
• B
• C
• D
• E

Q21:

In a class of 67 students, 54 passed a quiz. If 2 students are chosen at random from the entire class, what is the probability that at least one of them did NOT pass the quiz?

• A
• B
• C1
• D
• E