SOLUTION: You draw 5 cards from a standard deck (52 cards) without repetition. Find the probability of drawing at least 4 hearts, including the king of hearts.

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Question 1029765: You draw 5 cards from a standard deck (52 cards) without repetition. Find the probability of drawing at least 4 hearts, including the king of hearts.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
There are 5 possible ways of drawing 4 hearts, 1 non-heart
HHHHN
HHHNH
HHNHH
HNHHH
NHHHH
Within each of those there are 4 possible positions for the king of hearts so there are 20 (5*4) ways of drawing 4 hearts, one being the king of hearts.
The probability of each outcome is the same,
Let's work it out for KHHHN.
P%5B1%5D=%281%2F52%29%2812%2F51%29%2811%2F50%29%2810%2F49%29%2838%2F48%29
P%5B1%5D=2375%2F714714
There is one possible way of drawing 5 hearts but then there are 5 positions for the king of hearts.
P%5B2%5D=%281%2F52%29%2812%2F51%29%2811%2F50%29%2810%2F49%29%289%2F48%29
P%5B2%5D=33%2F866320
So then putting it all together,
P=20%2AP%5B1%5D%2BP%5B2%5D
P=20%282375%2F714714%29%2B33%2F866320
highlight%28P=1901089%2F28588560%29