Find the proability of getting a full house 3 cards of one

Find the proability of getting a full house ( 3 cards of one denomination and 2 of another) when 5 cards are dealt from an ordinary deck. Answer as a fraction

Solution

A poker hand consistes of 5 cards dealt from an ordinary deck of 52 playing cards. The number of possible ways is

52C5 = 2,598,960.

We required 3 cards of one denomination and 2 of another.

     There are 13 ways for the value of triple. Draw three cards from 4 card is 4C3=4

     There are 12 ways for the value of the pair. Ddraw two cards from 4 cards is 4C2=6

     Therefore, there are: 13 × 12 × 4 × 6 = 3,744 possible Full Houses

Now, P(Full House) = 3,744 / 2,598,960 = 0.001440576