| If ten friends shake hands mutually, then the total number of handshakes is |
A) 45
B) 50
C) 90
D) 100
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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