Question

A flush in a five card hand with all cards of the same suit.What is the probability of getting a flush?

Answer 1

that would simply be

C(4,1) * C(13,5) / C(52,5)
= 5148/2598960
= 99/49980
= 33/16660
= appr .00198

Note, I included the royal flush in the above, you did not say anything about exclusion.
What about other hands that are both a flush and something else?
e.g. what about the 4,5,6,7,8 of hearts?
that would be a flush, but also a straight.
To have a "pure flush", would involve a bit more calculations