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From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers, four persons are selected at random. The probability that selection contains one of each category is

Solution :

n(S) = 10C4 = 210

n(E)= 5C2×3C1×2C1 + 5C1×3C2×2C1 + 5C1×3C1×2C2 = 105

P(E) = 105\over 210 = 1\over 2


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