There are n married coupled at a party. Each person shakes hand with every person other than her or his spouse. Find the total number of hand shakes.

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Solution

Total hand shakes possible $=$ $^{2 n} C_{2}$ .
This will include n hand shakes in which a person shakes hand with her or his spouse.
$∴$ Required number $=$ $^{2 n} C_{2} - n = 2 n (n - 1)$ .

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There are n married coupled at a party. Each person shakes hand with every person other than her or his spouse. Find the total number of hand shakes.

Total hand shakes possible = 2nC2.This will include n hand shakes in which a person shakes hand with her or his spouse.∴ Required number = 2nC2−n=2n(n−1).

Total hand shakes possible $=$ $^{2 n} C_{2}$ .
This will include n hand shakes in which a person shakes hand with her or his spouse.
$∴$ Required number $=$ $^{2 n} C_{2} - n = 2 n (n - 1)$ .