Worksheet: Using Combinations to Find Probability

In this worksheet, we will practice finding the number of outcomes and the probability using combinations.

Q1:

Find the number of ways to select 3 different letters from the set { , , , , , , , } c d e f g h k j .

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

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 5 2 8
  • B 5 1 3
  • C 1 1 , 2 8 7
  • 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:

Dina 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 Engy, Sally, Farida, and Dalia are chosen?

  • A
  • B
  • C
  • D
  • E0

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. Adel 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 colour. If Amir selects four marbles from the bowl, what is the probability that he selects the marbles with the four colours that he wants?

  • A
  • B
  • C
  • D
  • E0

Q10:

Mariam 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:

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 4
  • B 6
  • C 7
  • D 5

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

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 4 1 5
  • B 4 7
  • C 1 3 5
  • 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 

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