# Counting Principles

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Section 8.1 #14

Section 8.2 #20,46

Section 8.3 #26

Section 8.4 #8,16

14. A menu offers a choice of 3 salads, 8 main dishes, and 5

desserts. How many different meals consisting of one

salad, one main dish, and one dessert are possible?

20. A group of 3 students is to be selected from a group of

12 students to take part in a class in cell biology.

a. In how many ways can this be done?

b. In how many ways can the group who will not take part

be chosen?

46. Pizza Varieties A television commercial for Little Caesars

pizza announced that with the purchase of two pizzas, one

could receive free any combination of up to five toppings

on each pizza. The commercial shows a young child waiting

in line at Little Caesars who calculates that there are

1,048,576 possibilities for the toppings on the two pizzas.*

a. Verify the child's calculation. Use the fact that Little

Caesars has 11 toppings to choose from. Assume that the

order of the two pizzas matters; that is, if the first pizza

has combination 1 and the second pizza has combination

2, that is different from combination 2 on the first pizza

and combination 1 on the second.

b. In a letter to The Mathematics Teacher, Joseph F. Heiser

argued that the two combinations described in part a

should be counted as the same, so the child has actually

overcounted. Give the number of possibilities if the

order of the two pizzas doesn't matter.

26. After studying all night for a final exam, a bleary-eyed student randomly grabs 2 socks

from a drawer containing 9 black, 6 brown, and 2 blue socks, all mixed together. What

is the probability that she grabs a matched pair?

Suppose that a family has 5 children. Also, suppose that the probability of having a girl is 1/2.

Find the probabilities that the family has the following children.

8. No more than 4 girls

A coin is tossed 6 times. Find the probabilities of getting the following.

16. Exactly 3 heads

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###### Education

- BSc, Meerut University
- MSc, Meerut University
- MPhil, Institute of Advanced Studies
- MSc, AIT

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