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## Homework Statement

A poker hand conatins 5 cards chosen from a deck of 52.

1. How many hands are possible

a. 4 of a kind

b.3 of a kind

c. flush

d. full house

e. straight

f. straight flush

## The Attempt at a Solution

When i write (5,2) I mean 5 choose 2 .

1. (52,5)

a. I have 13 different choices from 2 .... king, ace .

so (13,1)*(4,4)*(12,1)*(4,1) then my last card has to come from the remaining 12 and then of the 4 of those cards I have to pick 1 .

b. (13,1)(4,3)(12,1)(4,1)(11,1)(4,1)

When I pick my last cards I have to pick from different rows to avoid getting 4 of a kind or a full house.

c. I have 4 different suits to pick from so I pick 1 of the four then pick 5 of the suits 13 cards. so it will be (4,1)(13,5)

d. full house will be (13,1)(4,3)(12,2)

e. Well there are 9 ways to get a straight with 5 cards numerically in a row.

and their are 4 copies of an ace so i think the answer is 4^5(9)

f. well there are 9 ways to get a straight an 4 suits so 9*36 but it would be (9,1)(4,1)