Question

The correct expression of ${}^8{\text{C}}_4$ is

• A. $\frac{8\times 7\times 6\times 5\times 4}{1\times 2\times 3\times 4}$
• B. $\frac{8\times 7\times 6\times 5}{1\times 2\times 3\times 4}$
• C. $\frac{8\times 7\times 6\times 5\times 4}{1\times 2\times 3\times 4!}$
• D. $\frac{8\times 7\times 6\times 5!}{1\times 2\times 3\times 4!}$

Answer 1

The correct option is B $\frac{8\times 7\times 6\times 5}{1\times 2\times 3\times 4}$

Since, ${}^n{\text{C}}_r=\frac{n(n-1)(n-2)(n-3)\dots rterms}{1\times 2\times 3\times \dots rterms}$

Hence,
${}^8{\text{C}}_4=\frac{8\times 7\times 6\times 5}{1\times 2\times 3\times 4}$