Number of ways to get a flush from shuffled cards

Question

How many different ways are there to draw a flush from a well shuffled full deck of cards?

If correctly counting, I suppose the answer is $\frac{13\times 12\times 11 \times 10 \times 9}{1\times 2 \times 3 \times 4 \times 5}$, but would like to know your thoughts on it.

Answer 1

You can select $5$ cards from a suit in $\binom{13}5$ ways, and since there are $4$ suits, multiply it by $4$, which you did not.