Lesson Worksheet: Using Combinations 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 combinations.


Find the number of ways to select 3 different letters from the set {,,,,,,,}cdefghkj.


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


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.

  • A142
  • B14323
  • C1969
  • D14,845
  • E2969


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


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

  • A𝐶
  • B𝐶
  • C𝐶
  • D𝐶


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.

  • A542
  • B10729
  • C172
  • D2252
  • E112


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


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

  • A6!
  • B7!
  • C5!
  • D4!


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

  • A9
  • B8
  • C16
  • D64


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?

  • A1120
  • B120
  • C110
  • D1
  • E160

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