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1) Use the formula for Permutations, to find the value for each expression. Confirm each result by using your calculator.
a)
b)
c)
d)
2) How many 4 letter permutations can be formed from the letters in word rhombus?
3) For a board of directors composed of eight people, in how many ways can a president, vice president, and treasurer be selected?
4) How many different ID cards can be made if there are six digits on a card and no digit can be used more than once?
5) In how many ways can seven different brands of laundry soap be displayed on a shelf in a store?
6) A child has four different stickers that can be placed on a model car in a vertical stack. In how many ways can this be done if each sticker is to be used only one time?
7) An inspector must select three tests to perform in a certain order on a manufactured part. He has a choice of seven tests. How many different ways can he perform three tests?
8) In how many different ways can 4 raffle tickets be selected from 50 tickets if each of the 4 ticket holders wins a different prize?
[Figure4]
9) A researcher has 5 different antibiotics to test on 5 different rats. Each rat will receive exactly one antibiotic and no rat will receive the same antibiotic as any other rat. In how many different ways can the researcher administer the antibiotics?
10) There are five violinists in an orchestra. Three of them will be selected to play in a trio with a different part for each musician. In how many ways can the trio be selected?
11) There are five violinists in an orchestra. Four of them will be selected to play in a quartet with a different part for each musician. In how many ways can the quartet be selected?
12) There are five violinists in an orchestra. All five of them will be selected to play in a quintet with a different part for each musician. In how many ways can the quintet be selected?
13) There are five violinists in an orchestra. A piece of music is written so that it can be played with either 3, 4, or 5 violinists. Each musician selected to play this piece will play a different part. In how many ways can a group of at least three musicians be selected? Hint: Use your answers from problems 10), 11) and 12).
14) Decide whether each situation below involves permutations. Briefly explain your answers.
a) Sophia picks three color crayons from a box of 12 crayons to make a picture for her cat, Butterscotch.
b) A five-digit code is needed to open up an electronic lock on a car.
c) Twenty race car drivers must each complete three laps at a race track during a time trial, one after another, in order to establish the order in which the cars will start a race the next day.
d) There are seven steps that a student must follow when preparing cookies during their Family and Consumer Sciences course.
Review Exercises
15) Use the Fundamental Counting Principle to determine the number of different ways a person could order a meal if they are to pick one entree from four choices, one side order from three choices, and one drink from four choices.
16) A student wishes to check out three books from the library. She will check out one historical fiction book, one biography, and one book on art history. Build a tree diagram to show how many ways can this be done if there are two historical fiction books, three biographies, and two books on art history that she is considering checking out.
17) How many different outcomes are possible for the total on a roll of two dice if one die has 6 sides and one die has 4 sides?
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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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