If $15^k$ divides 47 ! but $15^{k+1}$ does not divide it, then $k=$

Since, $15=3 \times 5$, so to find the exponent of 15 in 47 ! It is enough to find the exponent of 5 in 47 !. So, exponent of 5 in 47 !. $=\left[\frac{47}{5}\right]+\left[\frac{47}{5^2}\right]+\ldots,\{$ where, $[x]$ is greatest integer of $x]$. $$ =9+1 $$ So, required value of $k$ is 10 . Hence, option (c) is correct.