# 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) = $$^{10}C_4$$ = 210

n(E)= $$^5C_2 \times ^3C_1 \times ^2C_1$$ + $$^5C_1 \times ^3C_2 \times ^2C_1$$ + $$^5C_1 \times ^3C_1 \times ^2C_2$$ = 105

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

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