Question

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

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is A 0

Exponent of 7 in 100! is
$=\left[\frac{100}{7}\right]+\left[\frac{100}{7^2}\right]+\left[\frac{100}{7^3}\right]=14+2=16$
Exponent of 7 in 50! is
$=\left[\frac{50}{7}\right]+\left[\frac{50}{7^2}\right]=8$
$\therefore$ Exponent of 7 in ${}^{100}{C}_{50}=\frac{100!}{50!50!}=\frac{7^{16}}{7^8{7}^8}=7^0$