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(B) To find the total number of handshakes,we need to choose $2$ people out of $15$ to perform a handshake. This is a combination problem because the

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$^{15}C_2$

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(B) To find the total number of handshakes,we need to choose $2$ people out of $15$ to perform a handshake. This is a combination problem because the order of the two people shaking hands does not matter. The number of ways to choose $2$ people out of $15$ is given by the combination formula $^{n}C_{r} = \frac{n!}{r!(n-r)!}$. Here,$n = 15$ and $r = 2$. Therefore,the total number of handshakes is $^{15}C_{2} = \frac{15 	imes 14}{2 	imes 1} = 105$.

There are $15$ people at a party and each person shakes hands with every other person. What is the total number of handshakes?

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