Chapter 12.6, Problem 41P

Determine which value is greater. ${}_9{C}_6$ or ${}_9{C}_5$

To determine

Determine which value is greater.

Answer to Problem 41P

  $C{}_6<C{}_5$

Explanation of Solution

Given:

  $C{}_{6}orC{}_5$

Formula Used:

  $C{}_r=\frac{n!}{r!(n-r)!}$

Calculation:

  $\begin{array}{l}C{}_6=\frac{9!}{6!(9-6)!}=\frac{9!}{6!3!}=\frac{9\cdot 8\cdot 7}{3\cdot 2}=84\\ C{}_5=\frac{9!}{5!(9-5)!}=\frac{9!}{5!4!}=\frac{9\cdot 8\cdot 7\cdot 6}{4\cdot 3\cdot 2}=126\end{array}$

and 84 < 126

So, $C{}_6<C{}_5$