Question

The exponent of $7$ in ${}^{120}{C}_{50}$, is

• A. $0$
• B. $2$
• C. $4$
• D. None of these

Answer 1

Answer: (A)

$0$

Exponent of $7$ in ${}^{120}{C}_{50}$

${}^n{C}_r=\frac{n!}{(n-r)!r!}{\Rightarrow }^{120}{C}_{50}=\frac{120!}{70!\times 50!}=\frac{120\times 119\times 118\times .....71}{50\times 49\times 48\times .....2\times 1}$

Number of multiples of $7$ in Numerator $=$ Denominator $=8$

Therefore Exponent of $7$ is $0$