When ten persons shake hands with one another | vedclass

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Question

(D) To find the number of handshakes,we need to choose $2$ persons out of $10$ to perform a handshake.This is a combination problem because the order

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(D) To find the number of handshakes,we need to choose $2$ persons out of $10$ to perform a handshake.This is a combination problem because the order of the two people shaking hands does not matter.The formula for combinations is given by $^nC_r = \frac{n!}{r!(n-r)!}$.Here,$n = 10$ and $r = 2$.Number of ways $= ^{10}C_2 = \frac{10 	imes 9}{2 	imes 1} = 45$.Therefore,there are $45$ possible ways for ten persons to shake hands with one another.

When ten persons shake hands with one another,in how many ways is it possible?

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