If $n$ ! has 17 zeros, then what is the value of $n$ ?

$\because$ number of zeroes $=$ Highest power of 5. $\therefore$ by using options highest power in 95 is $\left[\frac{95}{5}\right]+\left[\frac{95}{25}\right]+\left[\frac{95}{125}\right]=21$ highest power in 80 is $\left[\frac{80}{5}\right]+\left[\frac{80}{25}\right]=19$ highest power in 85 is $\left[\frac{85}{5}\right]+\left[\frac{85}{25}\right]=19$ $\therefore$ option (D) no such value of $n$ exists.