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.

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

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?

  • A11,287
  • B528
  • C513
  • D11840
  • 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?

  • A110,626
  • B56
  • C0
  • D16
  • E1255,024

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.

  • A542
  • B10729
  • C172
  • D2252
  • E112

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?

  • A112,650
  • B1303,600
  • C425
  • D0
  • E2125

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
  • B129,760
  • C14,960
  • D2932
  • E332

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?

  • A6!
  • B7!
  • C5!
  • D4!

Q13:

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!

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?

  • A135
  • B415
  • C47
  • D139
  • 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?

  • A1120
  • B120
  • C110
  • D1
  • E160

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.

  • A112
  • B172
  • C10729
  • D542
  • E1100

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