Question

use the formula for $_{n}c_{r}$ to evaluate the given expression.
$_{8}c_{5}$

$_{8}c_{5}=\square$ (type an integer or a simplified fraction.)

Explanation:

Step1: Recall combination formula

The formula for \( _nC_r \) is \( \frac{n!}{r!(n-r)!} \). Here, \( n=8 \), \( r=5 \).

Step2: Substitute values into formula

\( _8C_5 = \frac{8!}{5!(8-5)!} = \frac{8!}{5!3!} \)

Step3: Simplify factorials

\( 8! = 8×7×6×5! \), so cancel \( 5! \): \( \frac{8×7×6}{3!} = \frac{336}{6} = 56 \)

Answer:

56