How to solve this factorial equation?

Question

How to solve this factorial equation?

$$\frac{n!}{(n-6)!} = 350.418$$

or to give you the original equation:

$$0.146 = \binom{n}{6} \times 0.45^6 \times 0.55^{n-6}$$

Sorry, but I've no idea about LaTex

Answer 1

Here's the binomial distribution under your parameters. The closest answer is $n=17$ where the distribution value is $0.143168$: