Quantitative Aptitude Ques 2173

Question: If ten friends shake hands mutually, then the total number of handshakes is

Options:

A) 45

B) 50

C) 90

D) 100

Show Answer

Answer:

Correct Answer: A

Solution:

  • It is to be noted that, when two persons shake hands, it is counted as one handshake.

$ \therefore $ Total number of handshakes $ ={}^{10}C _2 $ $ \because $ $ {}^{n}C _{r}=\frac{n!}{r!(n-r)!}=\frac{10!}{2!(10-2)!} $ $ =\frac{10\times 9\times 8!}{2\times 1\times 8!}=\frac{10\times 9}{2}=45 $

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