Question

simplify the expression $_{6}c_{5}$. a. 6 b. 24 c. 30 d. 720 please select the best answer from the choices provided

Explanation:

Step1: Recall the combination formula

The combination formula is \(_{n}C_{r}=\frac{n!}{r!(n - r)!}\), where \(n! = n\times(n - 1)\times\cdots\times1\). Here \(n = 6\) and \(r=5\).

Step2: Substitute values into the formula

\(_{6}C_{5}=\frac{6!}{5!(6 - 5)!}=\frac{6!}{5!1!}\).
Since \(n!=n\times(n - 1)!\), then \(6! = 6\times5!\).
So \(_{6}C_{5}=\frac{6\times5!}{5!\times1}\).

Step3: Simplify the expression

Cancel out the \(5!\) terms. We get \(_{6}C_{5}=\frac{6}{1}=6\).

Answer:

A. 6