Question

The exponent of $7$ in ${}^{100}{C}_{50}$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (A)

We know that, ${}^{100}{C}_{50}=\frac{100!}{50!50!}$
The exponent of $7$ in $50!$ is
$\left[\frac{50}{7}\right]+\left[\frac{50}{7^2}\right]=7+1=8$
And the exponent of $7$ in $100!$ is
$\left[\frac{100}{7}\right]+\left[\frac{100}{7^2}\right]=14+2=16$
Thus, the exponent of $7$ in ${}^{100}{C}_{50}$ is $16-2\times 8=0$