Practice 1:Eight Pieces of Paper Are Numbered from 1 to 8 and Placed in a Box. One Piece

Practice 1:Eight pieces of paper are numbered from 1 to 8 and placed in a box. One piece of paper is drawn

from the box,its number is written down,and the piece of paper is replaced in the box. Then,a piece of paper

is again drawn from the box,and its number is written down. Finally,the two numbers are added together.

How many different ways can a total of 12 be obtained?

EXAMPLE 2 Eight pieces of paper are numbered from 1 to 8 and placed in a box. Two pieces of paper are drawn from the box,and the numbers on the paper are written down and totaled. How many different ways can a total of 12 be obtained?

Practice 3 How many different pairs of letters from the English alphabet are possible?

Number of Permutations of nElements

The number of permutations of nelements is In other words,there are n!different ways that nelements can be ordered.

Permutations of nElements Taken rat a Time

The number of permutations of nelements taken rat a timeis

Practice 4 Telephone numbers in the United States have 10 digits. The first three are the areacodeand the next seven are the local telephone number. How many different telephone numbers are possible within each area code? (Note that a local telephone number cannot begin with 0 or 1.)

Example 5 How many permutations are possible for the letters A,B,C,D,E,and F?

Practice 5b Eight horses are running in a race. In how many different ways can these horses come in first,second,and third? (Assume that there are no ties.)

Practice 6 In how many distinguishable ways can the letters in BANANA be written?

EXAMPLE 8 In how many different ways can three letters be chosen from the letters A,B,C, D,and E? (The order of the three letters is not important.)

Practice 8a.

A standard poker hand consists of five cards dealt from a deck of 52. How many different poker hands are possible?

Practice 8c

A restaurant serves omelets that can be ordered with any of the ingredients shown.

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a)aa a Suppose you want exactly 2 vegetarian ingredients and 1 meat ingredient in your omelet.

How many different types of omelets can you order?

II. Suppose you can afford at most 3 ingredients in your omelet. How many different

types of omelets can you order?

you2 vegetarian ingredients and 1 meat ingredient in your omelet. How many different types of omelets can you order?

Example 9. Find the total number of subsets of a set that has 10 elements

Practice 9b. A theater is staging a series of 12 different plays. You want to attend at least 3 of the plays.

How many different combinations of plays can you attend?

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