Question

question 6
calculate ( c _ { 8 } ^ { 3 } )
add your answer
integer, decimal, or e notation allowed

Explanation:

Step1: Recall combination formula

The combination formula is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 8\) and \(r=3\).

Step2: Calculate factorial values

\(n!=8! = 8\times7\times6\times5\times4\times3\times2\times1\), \(r!=3! = 3\times2\times1\), \((n - r)!=(8 - 3)!=5! = 5\times4\times3\times2\times1\). Then \(C(8,3)=\frac{8!}{3!×5!}=\frac{8\times7\times6\times5!}{3\times2\times1\times5!}\).

Step3: Simplify the expression

Cancel out \(5!\) in the numerator and denominator. \(\frac{8\times7\times6}{3\times2\times1}=\frac{336}{6}\).

Answer:

\(56\)