five cards are dealt from a well-shuffled deck of 52 cards . what is the probability that the hand will contain ;

Question

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1714

2

a) 2 tens and 3 fives ?

b) exactly 3 twos and two other cards that are not twos?

c) three of a kind ? [ three cards the same and two other cards not the same as the three of a kind and not the same as each other ]

Guest Dec 21, 2016

CPhill · Answer 1 · 2016-12-21T08:31:03

Here's (a) :

a) We choose three of the four fives = 4 ways to do this .... and two of the four tens = 6 ways to do this

This makes 4 x 6 = 24 such hands.......and there are C(52,5) = 2,598,960 possible hands....so the probability is : 24 / 2,598,960 = 1/108,290

CPhill · Answer 2 · 2016-12-21T08:44:49

Find the answer to (c) here : https://en.wikipedia.org/wiki/Poker_probability