1.4 Problem Set

1) Use the formula for combinations to find the value of each expression. Use a calculator to verify each answer.

a)

2) In how many ways can 3 cards be selected from a standard deck of 52 cards?

3) In how many ways can three bracelets be selected from a box of ten bracelets?

4) In how many ways can a student select five questions to answer from an exam containing nine questions?

[Figure4]

5) In how many ways can a student select five questions to answer from an exam containing nine questions if the student is required to answer the first and the last question?

6) The general manager of a fast-food restaurant chain must select 6 restaurants from 11 for a promotional program. In how many different possible ways can this selection be done?

7) There are 7 women and 5 men in a department. In how many ways can a committee of 4 people be selected?

8) For a fundraiser, a travel agency has donated 5 free vacations to Mexico as grand prizes in a raffle. Suppose that 220 people paid for raffle tickets. In how many different ways can the vacation winners be selected?

9) A high school choir has 27 female and 19 male members. Two students will be selected from the choir to represent the school in the All-State Choir.

a) In how many ways can the director select two students if she decides both students will be female?

b) In how many ways can the director select two students if she decides both students will be male?

c) In how many ways can the director select two students?

d) Using your answers from a), b) and c), determine how many ways the choir director can select two students such that one student will be a male and one student will be a female?

Review Exercises

10) In how many ways can the team captain of a kickball team arrange the kicking order for the 7 players on the team?

11) An electronic car door lock has five buttons on it and each button has a different digit. Suppose the combination to unlock the door is 4 digits long.

a) How many different combinations are possible if digits can be repeated?

b) How many different combinations are possible if digits cannot be repeated?

12) Give the sample space for the different results that may occur if a coin is flipped twice.

13) Decide whether each situation involves permutations.

a) A teacher must pick two students from a class of 30 to put their answers on the board for problem #11 from last night's homework.

b) In order to be allowed outside to play in the rain, a 5-year old must put on socks, shoes, and boots.

c) A student has a strict bedtime of 11 pm. They need two hours to finish writing a paper, one hour for a math assignment, and two hours for a science experiment. It is 6 pm right now.

Image Attributions

• [1]^ License: CC BY-NC 3.0
• [2]^ License: CC BY-NC 3.0
• [3]^ License: CC BY-NC 3.0
• [4]^ License: CC BY-NC 3.0

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