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Mr. X is selected for interview for 3 posts. For the first post there are 5 candidates, for the second there are 4 and for the third there are 6. If the selection of each candidate is equally likely, find the chance that Mr. X will be selected for atleast one post

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$\frac{1}{20}$

$\frac{119}{120}$

$\frac{1}{2}$

$\frac{1}{3}$

answer is D.

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Detailed Solution

A=first post

B=Second post

C=Third post

$P (A) = \frac{1}{5} P (B) = \frac{1}{4} P (C) = \frac{1}{6}$

P(at least one post) $= 1 - P$ (not selected any post)

$= 1 - (1 - \frac{1}{5}) (1 - \frac{1}{4}) (1 - \frac{1}{6}) = 1 - \frac{4}{5} \times \frac{3}{4} \times \frac{5}{6} = 1 - \frac{1}{2} = \frac{1}{2}$

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