Question

What is the value of ${}_7{\text{C}}_2?$

• A. $21$
• B. $18$
• C. $14$
• D. $49$

Answer 1

The correct option is A $21$

${}_7{\text{C}}_2=\frac{7!}{(7-2)!\times 2!}$

$=\frac{7!}{5!\times 2!}$

$=\frac{7\times 6\times 5!}{5!\times 2!}$

$=\frac{7\times 6}{2}$

$=7\times 3$

$=21$