[Math] How many $7$-digit telephone numbers with distinct digits starting with $927$ are there

Question

A telephone number consist of seven digits. How many phone numbers with distinct digits starting with 927 are there?

I answered $10^4$. Is that correct?

Answer 1

Since those numbers start with $927$ and the numbers are distinct you only can choose among $\{0,1,3,4,5,6,7,8\}$ distinctively $4$ more digits. Therefore the total number of such phone numbers is $$4!\binom{7}{4}=\dfrac{7!}{3!}=840$$