Question

If you are dealing from a standard deck of 52 cards a) how many different 4-card hands could have at least one card from each suit? b)how many different 5-card hands could have at least one spade? c) how many different 5-card hands could have at least two face cards (jacks, queens or kings)?

Answer 1

a) We need one card from each suit as there are 4 suits, we are playing 4 card hands so one from each will come.

There are 13 cards in a suit.

So, total ways = 13*13*13*13 =28561 different 4-card hands

b) Total 5 card hands =

Total 5 cards hands when no spade =

So, total 5 cards hands with atleast one spade = 2598960 - 575757 = 2023203

c) Total 5 card hands = 2598960 (From part b)

Total face cards = 4*3 = 12

Total ways with 0 face card =

Total ways with 1 face card =

So, total ways with at least two face cards = 2598960 - 658008 - 1096680 = 844272