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?
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Practice 3 How many different pairs of letters from the English alphabet are
possible?
Number of Permutations of n Elements
The number of permutations of n elements is
words, there are n! different ways that n elements can be ordered.
In other
Permutations of n Elements Taken r at a Time
The number of permutations of n elements taken r at a time is
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Practice 4 Telephone numbers in the United States have 10 digits. The first three are
the area code and 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?
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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?
Practice 6b. 3 red chairs (exactly the same), 5 green chairs(exactly the same) and 2
pink chairs(exactly the same). How many ways can be arranged?
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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 8b.
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Practice 8c
A restaurant serves omelets that can be ordered with any of the ingredients shown.
111
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?
you
2 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
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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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