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 Problem: A bag contains 5 blue and 4 black balls. Three balls are drawn at random, what is the probability that 2 are blue and 1 is black? [ Calculator, Method and examples ]Solution:Your problem -> A bag contains 5 blue and 4 black balls. Three balls are drawn at random, what is the probability that 2 are blue and 1 is black?Total number of balls=5+4=9Let S be the sample space. Then, n(S) =  Total number of ways of drawing 3 balls out of 9 :.n(S) = {::}^9C_3=(9 * 8 * 7)/(3 * 2 * 1)=84Let E= Event of drawing 2 blue balls out of 5 and 1 black balls out of 4.n(E) = {::}^5 C_2 xx {::}^4 C_1=(5 * 4)/(2 * 1) xx 4=10 xx 4=40:.P(E)=(n(E))/(n(S))=40/84=10/21

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