(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A poker hand contains five cards dealt from a deck of 52. How many distinct poker hands can be dealt containing:

a) two pairs (for example 2 kings, 2 aces, and a 3)

b) a flush (five cards in a given suit)

c) a straight flush (any five in sequence in a given suit, but not including ten, jack, queen, king, ace)

d) a royal flush (ten, jack, queen, king, ace in a single suit)

3. The attempt at a solution

Essentially, I am asked to form distinct 5 tuples with certain criteria.

a) I've made a tree. Please tell me if there is a simpler way. Each (dot) on the tree tells you how many choices you can make at that given point. Whenever the tree branches, it goes into the various choices you can make.

For the other solutions also, I've made similar trees, but I feel this a long way. Does anyone have any other shorter methods?

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# Problem in Combinatorics

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