[Math] Probability of same suit if drawing $5$ cards from deck of $52$ cards

Question

If we draw $5$ cards from a standard deck of $52$ cards without replacement, find the probability of drawing all cards of the same suit.

I think the answer is $P(\text{same suit})=\frac{13}{52}\times\frac{12}{51}\times\frac{11}{50}\times\frac{10}{49}\times\frac{9}{48}$.

Is this at least close to correct?

Answer 1

You are on the right track. You just need to multiply your answer by 4 since there are 4 suits.