14111cn6.9-11

# 14111cn6.9-11 - Example 5 How many ﬁve-digit numbers can...

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c ± Kendra Kilmer September 16, 2011 Section 6.3 - Multiplication Principle Example 1: A yogurt shop has 3 ﬂavors (Chocolate, Vanilla, and Strawberry) and two sizes (Large and Medium). How many different yogurts can be ordered? Multiplication Principle: Suppose a task T 1 can be performed in N 1 ways, a task T 2 can be performed in N 2 ways, ... , and a task T n can be performed in N n ways. Then, the number of ways of performing the tasks T 1 , T 2 ,. . . , T n in succession is given by the product: Example 2: A coin is tossed 3 times, and the sequence of heads and tails is recorded. Determine the number of outcomes. Example 3: An auto manufacturer has 3 different subcompact cars in the line. Customers selecting one of these cars have a choice of 3 engine sizes, 4 body styles, and 3 color schemes. How many different selections can a customer make? 9

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c ± Kendra Kilmer September 16, 2011 Example 4: How many three-letter words that have exactly one vowel can be made using the ﬁrst seven letters of the alphabet where using a letter twice is permitted but having two consonants next to each other is not?
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Unformatted text preview: Example 5: How many ﬁve-digit numbers can be formed if a) Zero is not the ﬁrst digit? b) Zero cannot be the ﬁrst digit and no digit can be repeated? c) Zero cannot be the ﬁrst digit, no digit can be repeated, and each number formed must be even? 10 c ± Kendra Kilmer September 16, 2011 Example 6: Jack and Jill and 5 of their friends go to the movies. They all sit next to each other in the same row. How many ways can this be done if a) there are no restrictions? b) Jill must sit in the middle? c) Jill sits on one end of the row and Jack sits on the other end of the row? d) Jack, Jill, or John sit in the middle seat? e) Jack, Jill, and John sit in the middle seats? f) Jack and Jill must sit next to each other? g) Jill must not sit next to Jack? Section 6.3 Highly Suggested Homework Problems: 1, 3, 5, 7, 9, 11, 15, 19, 21, 23, 25, 27, & Counting Handout 1 11...
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## This note was uploaded on 03/27/2012 for the course MATH 141 taught by Professor Jillzarestky during the Fall '08 term at Texas A&M.

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14111cn6.9-11 - Example 5 How many ﬁve-digit numbers can...

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