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Worksheet: Finding Probability Using Combinations

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 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:

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

Q5:

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

  • A
  • B
  • C
  • D

Q6:

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

  • A
  • B
  • C
  • D

Q7:

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

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 Liam 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
  • D
  • E0

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?

  • A
  • B
  • C
  • D
  • E0

Q11:

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

Q12:

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
  • C
  • D
  • E0

Q13:

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

Q14:

In a science fair experiment, three units are selected for testing out of every 587 units produced. In how many ways can these three units be selected?

Q15:

In a science fair experiment, three units are selected for testing out of every 517 units produced. In how many ways can these three units be selected?

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