BPSC 48th to 52nd Exam Prelims 2008 Solved Paper

Question : 39 of 150

Marks: +1, -0

The number of ways of dividing 15 men and 15 women into 15 couples each, consisting of a man and a woman is :

Solution:

First group may be chosen in

15 {c}_{1} × 15 {c}_{1}=15 × 15=225

The second group may be chosen in

14 {c}_{1} × 14 {c}_{1}=14 × 14=196

∴

Total number of ways

=15^{2}+14^{2}+13^{2}+. . . . . . . .+1^{2}

=\;{15(15+1)(15 × 2+1)}/{6}

=\;{15 × 16 × 31}/{6}=1240

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