How many different flush hands can you have that consist only of hearts, diamonds or spades?

Question

In poker, a flush is a 5-card hand where all the cards have the same suit. Recall that a deck of cards has 52 cards. There are 4 suits (hearts, clubs, diamonds and spades) and each suit has 13 cards.

How many ways can you get a flush of hearts, diamonds or spades?

For this question, I am thinking the answer is 13C5+13C5+13C5 where C is choses.I am not so sure because it looks tricky

Answer 1

It is exactly as you wrote: $13\choose5$ counts the number of different ways to get 5 cards out of that particular suit. This is the same for any suit, and so if you're interested in those particular flushes, the answer is as you gave: $3\cdot {13\choose 5}$.

Answer 2

There are indeed $_{13}C_5$ ways to have a flush hand of any given suit, and flushes of different suits are mutually exclusive events. Thus, just adding them up (as you did) works fine!

Answer 3

That's it =)

So $$3 \cdot {13 \choose 5}$$

Answer 4

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The total no of flushes possible are:$4\times ^{13}C_5$ and the favourable are $3\times^{13}C_4$
Chance for flush:

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http://en.wikipedia.org/wiki/Hand_rankings#Flush