Question

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

• A. 10
• B. 55
• C. 121
• D. 248

Answer 1

The correct option is B 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.

= $\frac{(n\times (n-1\left)\right)}{2}$

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

$=\frac{11\times 10}{2\times 1}$

= 55