Question

If the 11 teams members of a cricket team shake hands with each other. The total number of handshakes would be:

• A. 10
• B. 33
• C. 55
• D. 120

Answer 1

The correct option is C 55

Method 1:
If there are n people in a group,The first person shakes hands with a total of (n-1) persons, the second with (n-2) persons and so on.
So, total no. of handshakes $=(n-1)+(n-2)+(n-3)+.....+2+1.=(n\times (n-1\left)\right)\times 2$
Here, n=11.
So, the total no. of handshakes $=\frac{(11\times 10)}{2}=55$
Method 2 (Using Combinations)
Total no. of handshakes = no. of ways of selecting 2 people out of n.
= nC2
=11C2
$=\frac{(11\times 10)}{1\times 2}=55$