A poker hand consists of 5 cards drawn from a deck of 52 pla

A poker hand consists of 5 cards drawn from a deck of 52 playing cards. The hand is said to be \"full house\" if there are 3 cards of another. For example, three 10\'s and two jacks form a full house. How many such hands are possible?

Solution

We know that there are A in 4 of clubs, spade, dice, and hearts like that each card A,2,.....K

3 cards of the same type can be formed in 13C3 ways. ( as 13 sets of 4 are there)

Hence 3 same values can be got in 13(4c3) ways

The remaining cards two can be in any of 48 x 47 cards

Hence total no of hands = 13(4C3) 48x47

= 117312