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Chapter 5 Section 4

Chapter 5 Section 4. The Multiplication Principle. Generalized Multiplication Principle. If a task consists of t operations performed consecutively, then the task can be performed in m 1 • m 2 • m 3 • m 4 • … • m t ways. Trick is to identify the task and the operations.

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Chapter 5 Section 4

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  1. Chapter 5 Section 4 The Multiplication Principle

  2. Generalized Multiplication Principle • If a task consists of toperations performed consecutively, then the task can be performed in m1• m2• m3• m4• … • mt ways. • Trick is to identify the task and the operations.

  3. Exercise 3 (page 228) • How many two-letter words (including non-sense words) can be formed? Note: • Task: Form two-letter word • Two operations • Write the first letter • Write the second letter • Restriction(s): None Solution: 26• 26 = 676

  4. Exercise 7 (page 228) • Have 5 different pairs of gloves • How many ways can you select a right-handed glove and a left-handed glove such that they don’t match? Note: • Task: Select two gloves • Two operations • Pick the right-handed glove • Pick the left-handed glove • The authors assume that you pick the right-handed glove first. • Restriction(s): The two gloves can not match

  5. Exercise 7 Solution __ • __ = # of ways For selecting the right-handed glove: 5• _ For selecting the left-handed glove: 5• 4 Answer: 5• 4 = 20

  6. Exercise 11 (page 228) • Toss a coin 6 times and observe the sequence of heads and tails. How many different sequences? Note: • Task: Observe the sequence of heads and tails • Six operations • First coin toss • Second coin toss (etc.) 6. Sixth coin toss • Restriction(s): None

  7. Exercise 11 Solution Task: __ • __ • __• __• __ • __ Answer: 2• 2• 2• 2• 2• 2 = 26 = 64

  8. Exercise 23 Part (b) (page 229) • Set: { h , o , t , s , m , x , e } • How many four letter words (including nonsense words) can be formed with the restriction: Letters cannot repeat. Solution: 7• 6• 5• 4 = 840

  9. Exercise 23 Part (c) (page 229) • Set: { h , o , t , s , m , x , e } • How many four letter words (including nonsense words) can be formed with the restriction: Begins with ‘h’ and repetitions are allowed. Solution: 1• 7• 7• 7 = 343

  10. Exercise 23 Part (d) (page 229) • Set: { h , o , t , s , m , x , e } • How many four letter words (including nonsense words) can be formed with the restrictions: Word must end in vowel and repetitions are not allowed. Solution: 6• 5• 4• 2 = 240

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