d20 natural 1 specific question

Question

I think this is quite a difficult problem, but here goes:

If you roll $54$ $20$-sided dice, what is the probability of rolling a $1$ 10 times?

Answer 1

You can use the binomial distribution to solve this question. The probability $p$ of hitting $1$ equals $\frac{1}{20},$ so the probability of rolling this value $10$ times in $54$ rolls equals:

$${54 \choose 10} \bigg(\frac{1}{20}\bigg)^{10} \bigg(\frac{19}{20}\bigg)^{44} \approx 0.000245$$