Question

evaluate each expression. sample problem ( _8p_3 ) ( \frac{8!}{(8-3)!} = \frac{8!}{5!} = 336 ) ( _6c_5 ) enter the answer in the space provided. use numbers instead of words.

Explanation:

Step1: Recall the combination formula

The formula for combinations is \( _nC_r=\frac{n!}{r!(n - r)!} \). For \( _6C_5 \), we have \( n = 6 \) and \( r=5 \).

Step2: Substitute into the formula

Substitute \( n = 6 \) and \( r = 5 \) into the formula: \( _6C_5=\frac{6!}{5!(6 - 5)!} \).

Step3: Simplify the factorials

First, calculate \( 6-5 = 1 \), so \( (6 - 5)!=1!=1 \). Then, \( 6! = 6\times5! \), so the expression becomes \( \frac{6\times5!}{5!\times1!} \).

Step4: Cancel out common terms

The \( 5! \) in the numerator and denominator cancels out, leaving \( \frac{6}{1}=6 \).

Answer:

6