Four boys and three girls stand in a queue for an interview, probability that they will in alternate

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14.Probability

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Four boys and three girls stand in a queue for an interview, probability that they will in alternate position is

A

$\frac{1}{{34}}$

B

$\frac{1}{{35}}$

C

$\frac{1}{{17}}$

D

$\frac{1}{{68}}$

Solution

(b) Four boys can be arranged in $4\,!$ ways and three girls can be arranged in $3\,!$ ways.

$\therefore $ The favourable cases $ = 4\,!\, \times \,3\,!$

Hence the required probability $=\frac{{ 4\,!\, \times 3\,!}}{{7\,!}} = \frac{6}{{7 \times 6 \times 5}} = \frac{1}{{35}}$.

Standard 11

Mathematics

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