Chapter 0.4, Problem 8E

To determine

To find: Evaluate the combination $C_7^{12}=792$ .

Answer to Problem 8E

  $C_7^{12}=792$

Explanation of Solution

Given information: $C_7^{12}$

Formula used: $C_r^n=\frac{n!}{(n-r)!r!}$

Calculation:

Substitute the values of n and r into the formula.

  $C_7^{12}=\frac{12!}{(12-7)!7!}$

Simplify the right side

  $=\frac{12!}{5!7!}$

  $=\frac{12*11*10*9*8*7!}{5*4*3*2*1*7!}$

  $=\frac{12*11*10*9*8}{5*4*3*2*1}$

  $=\frac{12*11*2*3}{1}$

  $=792$

Hence $C_7^{12}=792$