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In a game of $5$-card draw poker, a player is dealt five cards from a deck of $52$ cards (without regard to order) How many ways are there to get a flush (five cards of the same suit)?

I know that I have to select $1$ suit and $5$ cards from that suit, so I proceded like that: $(^4C_1)\times(^{13}C_5)$

but the answer is: $(^4C_1)\times(^{13}C_5) - (10(4))$

I don't know where the $4$ and the $10$ are coming from

Any tip would be appreciated.

Maadhav
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Mahamad A. Kanouté
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    Please use MathJax (e.g. {13 \choose 5} for ${13 \choose 5} $). That will (hopefully) make it clearer what (10(4)) is. –  Dec 07 '17 at 18:41
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    You have to remove the straight flushes. – Randall Dec 07 '17 at 18:42
  • I still don't see why I have to remove anything and I don't know why we're multiplying 4 by 10. Intuitively I don't see any relation between the two – Mahamad A. Kanouté Dec 07 '17 at 18:50
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    Count the number of straight flushes (which are not technically flushes) by suit and low card. This is $4 \times 10$. – Randall Dec 07 '17 at 18:53
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    https://en.m.wikipedia.org/wiki/List_of_poker_hands - this problem is more about poker than about math. –  Dec 07 '17 at 18:57

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