Deck 6: Counting

Question 1

How many ways are there to choose five doughnuts if there are eight varieties (and only the type of each doughnut matters)?

Answer 1

The number of different ways to choose five doughnuts from eight different varieties equals the number of 5-combinations with repetition allowed from a set with 8 elements. This equals

Question 2

Answer 2

Question 3

What is the coefficient of

Answer 3

Question 4

Question 5

Each locker in an airport is labeled with an uppercase letter followed by three digits. How many different labels for lockers are there?

Question 6

There are 805 lockers in the athletic center and 4026 students who need lockers. Therefore, some students must share lockers. What is the largest number of students who must necessarily share a locker?

Question 7

(a) How many ways are there to arrange the letters of the word NONSENSE ? (b) How many of these ways start or end with the letter O ?

Question 8

How many different license plates can be made if each license plate consists of three letters followed by three digits or four letters followed by two digits?

Question 9

Find the value of each of the following quantities.

Question 10

How many rows are found in a truth table involving nine different propositions?

Question 11

How many students must be in a class to guarantee that at least five were born on the same day of the week?

Question 12

How many different string can be made using all the letters in the word GOOGOL?

Question 13

(a) How many ways are there to choose 12 cookies if there are five varieties of cookies?

Question 14

(a) How many functions are there from a set with three elements to a set with eight elements? (b) How many one-to-one functions are there from a set with three elements to a set with eight elements? (c) How many onto functions are there from a set with three elements to a set with eight elements?