SOLUTION: Consider being dealt 7 cards from a standard deck of 52. What is the probability that you will have at least on heart?

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Question 31205: Consider being dealt 7 cards from a standard deck of 52. What is the probability that you will have at least on heart?
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
IN PROBLEMS ASKING FOR PROBABILITY OF ATLEAST ONE HAPPENING,IT IS EASIER TO CACULATE,PROBABILITY OF NONE HAPPENING AND THEN SUBTRACT IT FROM ONE TO GET THE ANSWER.
SO LET US FIND PROBABILITY OF GETTING NO HEART
TOTAL COMBINATIONS OF 7 CARDS = 52C7=52!/7!(52-7)!=52*51*50*49*48*47*46/7!
NUMBER OF COMBINATIONS WITH NO HEART=39C7=39!/(39-7)!7!=39*38*37*36*35*34*33/7!
PROBABILITY OF GETTING NO HEART = 39*38*37*36*35*34*33/(52*51*50*49*48*47*46)=0.115
PROBABILITY OF GETTING ATLEAST ONE HEART = 1-0.115=0.885