Question

In a party, there are 15 members. Each shakes hand
with one another. Total numbers of the handshakes
is
(1) 120 (2) 105
(3) 90 (4) 15

Answer 1

Solution:

To find the total combination of hand shake ,we have to used formula of combination

$\rm^nC_{r} = \frac{n!}{r!(n - r)!}$
Total members in the party = 15

For a handshake members required = 2

Apply in Formula
$\rm^{15}C_{2}= \frac{15!}{2!(15 - 2)!} \\ \\ = \frac{15 \times 14 \times 13!}{2! \times13! } \\ \\ = 15 \times 7 \\ \\ = 105$
Total numbers of handshake = 105

Thus option (2) is correct.

Hope it helps you.