At a party, everyone shook hands with everyone else. It was found that $66$ handshakes were exchanged. The number of persons who attended the party was

10

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12

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Solution

The correct option is B $12$
Handshake requires two persons. Therefore,
$^{n} C_{2} = 66$
or, $\frac{n!}{(n - 2)! 2!} = 66$
or, $n (n - 1) = 66 \times 2$
$= 132$
$∴ n = 12$

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At a party, everyone shook hands with everyone else. It was found that 66 handshakes were exchanged. The number of persons who attended the party was

The correct option is B 12Handshake requires two persons. Therefore, nC2=66or, n!(n−2)!2!=66or, n(n−1)=66×2=132∴n=12

At a party, everyone shook hands with everyone else. It was found that $66$ handshakes were exchanged. The number of persons who attended the party was

The correct option is B $12$
Handshake requires two persons. Therefore,
$^{n} C_{2} = 66$
or, $\frac{n!}{(n - 2)! 2!} = 66$
or, $n (n - 1) = 66 \times 2$
$= 132$
$∴ n = 12$