Probability with Combinations and Permutations

A parent-teacher committee consisting of four people is to be selected from fifteen parents and five teachers. Find the probability of selecting two parents and two teachers.

You are dealt 5 cards from a standard deck of playing cards. What is the probability you are dealt a flush?

**A flush is all 5 cards of the same suit (order does not matter).

• 1/1287

• 1/2598960

• 33/66640

• 5/52

There are 7 students in a class: 5 boys and 2 girls.
If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a boy?

• 5/7
• 1/7
• 2/7
• 1

There are 10 men and 6 women working at a company. A hiring committee of 4 staff members is selected by a supervisor.

What is the probability that the committee is made up of 3 women and 1 man?

• 10/91

• 1/20

• 3/16

• 36/91

Determine whether the question would be a permutation or combination: To complete a quiz, you must answer 3 questions from a list of 6 questions. In how many ways can you complete the quiz?

• Permutation

• Combination

• Neither

Determine whether the question would be a permutation or combination: Thirty-two students have applied to serve on student council, where all the positions are the same. There are only 6 openings. How many ways could the openings be filled?

• Combination

• Permutation

• Neither

Five comedians (Joe, Beth, Seth, Lucial, and Darth) are planning a show. The order of each performance is randomly selected. What is the probability that Joe will go second and Beth will go last? Write the answer as a simple fraction.

Five comedians (Joe, Beth, Seth, Lucial, and Darth) are planning a show. The order of each performance is randomly selected. What is the probability that Joe will go second? Write the answer as a simple fraction.

How many different permutations can be made from the letters of the word COMMUNICATION?

The model of car you are thinking of purchasing is available in nine different colors, three different styles and two sizes of motor. How many ways can you order the car?

• 15

• 18

• 54

• 729