Worksheet: Using Combinations to Find Probability

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 {,,,,,,,}cdefghkj.

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 1 4 2
  • B 1 4 3 2 3
  • C 1 9 6 9
  • D 1 4 , 8 4 5
  • E 2 9 6 9

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 1 1 , 2 8 7
  • B 5 2 8
  • C 5 1 3
  • D 1 1 8 4 0
  • 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 1 1 0 , 6 2 6
  • B 5 6
  • C0
  • D 1 6
  • E 1 2 5 5 , 0 2 4

Q7:

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

  • A    𝐶
  • B    𝐶
  • C    𝐶
  • D    𝐶

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 5 4 2
  • B 1 0 7 2 9
  • C 1 7 2
  • D 2 2 5 2
  • E 1 1 2

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 1 1 2 , 6 5 0
  • B 1 3 0 3 , 6 0 0
  • C 4 2 5
  • D0
  • E 2 1 2 5

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 1 2 9 , 7 6 0
  • C 1 4 , 9 6 0
  • D 2 9 3 2
  • E 3 3 2

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 6 !
  • B 7 !
  • C 5 !
  • D 4 !

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 9 !
  • B 8 !
  • C 1 6 !
  • D 6 4 !

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 1 3 5
  • B 4 1 5
  • C 4 7
  • D 1 3 9
  • E0

Q15:

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

  • A    𝐶
  • B    𝐶
  • C    𝐶
  • D    𝐶

Q16:

Chloe 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 1 1 2 0
  • B 1 2 0
  • C 1 1 0
  • D1
  • E 1 6 0

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 1 1 2
  • B 1 7 2
  • C 1 0 7 2 9
  • D 5 4 2
  • E 1 1 0 0

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