Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 6 - Section 6.4 - Binomial Coefficients and Identities - Exercises - Page 421: 13

Answer

1 9 36 84 126 126 84 36 9 1

Work Step by Step

The row of $(_k^9)$ is the binomial coefficients evaluated at k = 1,2,3,4,5,6,7,8, and 9. Thus: $(_0^9) = \frac{9!}{0!(9-0)!}$ = 1 $(_1^9) = \frac{9!}{1!(9-1)!}$ = 9 $(_2^9) = \frac{9!}{2!(9-2)!}$ = 36 $(_3^9) = \frac{9!}{3!(9-3)!}$ = 84 $(_4^9) = \frac{9!}{4!(9-4)!}$ = 126 $(_5^9) = \frac{9!}{5!(9-5)!}$ = 126 $(_6^9) = \frac{9!}{6!(9-6)!}$ = 84 $(_7^9) = \frac{9!}{7!(9-7)!}$ = 36 $(_8^9) = \frac{9!}{8!(9-8)!}$ = 9 $(_9^9) = \frac{9!}{9!(9-9)!}$ = 1
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