Question

Which of the following expression is equivalent to $\frac{n!}{(n-p)!\times p!}$?

• A. $\frac{n\times (n-1)(n-2)(n-3)\dots pterms}{1\times 2\times 3\times \dots pterms}$
• B. $\frac{n\times (n-1)(n-2)(n-3)\dots pterms}{1\times 2\times 3\times \dots nterms}$
• C. $\frac{n\times (n-1)(n-2)(n-3)\dots nterms}{1\times 2\times 3\times \dots pterms}$
• D. None of the above

Answer 1

The correct option is A $\frac{n\times (n-1)(n-2)(n-3)\dots pterms}{1\times 2\times 3\times \dots pterms}$

Since, ${}^n{\text{C}}_p=\frac{n!}{(n-p)!\times p!}$

And it can also be written as:

${}^n{\text{C}}_p$$=\frac{n\times (n-1)(n-2)(n-3)\dots pterms}{1\times 2\times 3\times \dots pterms}$

Example $\Rightarrow$
${}^5{\text{C}}_3=\frac{5\times 4\times 3}{1\times 2\times 3}$