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Homework_1_Solution

# Homework_1_Solution - STAT/MATH 418 Solution to Homework 1...

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Chapter 1 6. 7 7 7 7 2401 . = 7. (a) 6! 720 = (b) 2 3! 3! 72 = �� (c) 4!3! 144 = (d) 6 3 2 2 1 1 72 = ����� 9. (12)! 27,720 6!4! = 15. 10 12 199,584 5 5 � �� � = � �� � � �� � ( or the answer could be 10 12 5! 5 5 � �� � � �� � � �� � if we consider “paired them off”.) 21. 7! 35 3!4! = . Each path is a linear arrangement of 4r’s and 3u’s (r for right and u for up). For instance the arrangement r, r, u, u, r, r, u specifies the path whose first 2 steps are to the right, and final step is up. 26. ( 29 ( 29 ( 29 ( 29 1 2 3 1 2 3 4 1 2 3 1 2 3 4 1 2 3 4 2 3 2 3 , , n n n n n n x x x x x x n n n + + = + + = ° ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 4 0 0 0 4 0 0 0 4 1 2 3 1 2 3 1 2 3 3 1 0 3 0 1 0 3 1 1 2 3 1 2 3 1 2 3 1 3 0 1 0 3 1 2 3 1 2 3 4 4 4 2 3 2 3 2 3 4,0,0 0,4,0 0,0,4 4 4 4 2 3 2 3 2 3 3,1,0 3,0,1 0,3,1 4 4 4 2 3 2 3 1,3,0 1,0,3 0,1,3 x x x x x x x x x x x x x x x x x x x x x x x x = + + + + + + + + ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29
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