Question

A box contains 6 red, 4 white and 5 black balls. a person draws 4 balls. find the probability of there is atleast one ball of one color

Answer 1

A box contains 6 red, 4 white and 5 black balls. A person draws 4 balls from the box at random. Find the probability that among the balls drawn there is at least one ball of each color? 
# of ways to get 4 balls:: 15C4 = 1365
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# of ways to get 4 balls with no two of the same color::
# of red/white + red/black + white/black 
10C4 + 11C4 + 9C4 = 210 + 330 + 126 = 666 ways
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# of ways to get 4 balls WITH some balls of the same color:: 1365-666 = 699
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P(4 with at least one of each color) = 699/1365
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Hope This Helps :)