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Homework 6 Solutions

# Homework 6 Solutions - Solutions to Homework Six CS 191...

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Solutions to Homework Six CS 191 : Discrete Structures I Apr. 17 , Winter 2007 Due Date: Apr. 26, 2007, Thursday, before the class meeting. Section 6.6, p265 In Exercise 1-3, determine the number of strings that can be formed by ordering the letters given. Exercise (2) SCHOOL Answer : There are 1 S, 1 C, 1 H, 2 Os, 1 L Therefore, the answer is ! 2 ! 6 =360. Exercise (5) How many strings can be formed by ordering the letters SALESPERSONS if no two S’s are consecutive? Answer : We consider a two-step procedure. (1) We form strings in which no S occurs. This can be done in (8!/2!) ways. (2) We then place the four S’s in the seven in-between positions and two ending positions. This can be done in C(9, 4) ways. Therefore, the answer is C(9, 4) × 8!/2! = ! 4 6 7 8 9 × × × × 8!/2! = 2,540,160. Exercises 15-21 refer to piles of identical red, blue, and green balls where each pile contains at least 10 balls. 1

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Exercise (19) In how many ways can 10 balls be selected if exactly one red ball and at least one blue ball must be selected? Answer : This problem is equivalent to how many ways we can select 9 balls from the blue balls and green balls with a condition that at least one blue ball must be selected. This question is also equivalent to how many ways we can select 8 balls from the blue balls and green balls. Therefore, the answer is C(8+2-1, 8) = C(9, 1) = 9. In Exercises 22-29, find the number of integer solutions of x 1 + x 2 + x 3 = 15 subject to the conditions given.
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Homework 6 Solutions - Solutions to Homework Six CS 191...

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