Question

Thew exponent of $7$ in ${}^{100}{C}_{50}$ is_____

Answer 1

${}^{100}{C}_{50}=\frac{100!}{50!50!}$

$100!=k\times 7^{16}$

For some no. k

Similarity $50!=a\times 7^8$

So, ${}^{100}{C}_{50}=\frac{k\times 7^{16}}{a^2\times 7^{16}}=\frac{k}{a^2}$

Here $\frac{k}{a^2}$ is independent of factor of $7$

So, the exponent of $7$ in ${}^{100}{C}_{50}$ is zero $\left(0\right)$