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jamsey

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Poker hand question using combination?

Find the number of different poker hands that contain exactly 3 aces, while the remaining two cards do not form a pair?

find the number of pokerhands with two pairs with the fifth card a third different kind?

if you guys could explain the answers as well, that would be awesome.

Posted 781 day ago

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Answers (2)

fullhouse 		q1
[from 4 aces, choose 3]*
[from 12 other ranks, choose 2]*
[from 4 of 1st rank, choose 1]*
[from 4 of 2nd rank, choose 1]

= 4C3*12C2*(4C1)^2
= 4*66*16
= 4224
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q2
in a similar way,
[from 13 ranks, choose 2]*
[from 4 of 1st rank, choose 2]*
[from 4 of 2nd rank, choose 2]*
[from 11 remaining ranks, choose 1]*
[from 4 of rank, choose 1]

= 13C2*(4C2)^2 *11C1*4C1
= 123,552
---------------

Posted 781 day ago

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smithy 		find the number of poker hands with two pairs with the fifth card a third different kind?
Choose 3 aces in 4C3 ways. There are 48 cards left.
The fourth card may be chosen in 48 ways. The fifth card may be chosen in 44 ways since it should not be the same as the fourth card.
4 x 48 x 44 = 8,448 ways.

find the number of poker hands with two pairs with the fifth card a third different kind?

Choose the first pair in 4C2 (13) = 78 ways
Choose the second pair in 4C2 (12) = 72 ways
There are 40 cards left different from the ones already chosen. = 40 ways
78 x 72 x 40 = 224,640 ways.

Posted 781 day ago

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