How many handshakes are there when 15 people shake hands with each other?

To determine how many handshakes occur when 15 people shake hands with each other, we can use a mathematical concept involving combinations.
In any group of people, a handshake involves a pair, and the number of possible pairs among 'n' people is given by the combination formula:
Number of Handshakes = ( 2 n ​ ) = 2 n ( n − 1 ) ​
For the specific case where there are 15 people:

Substitute the value of n = 15 into the formula:
2 15 × 14 ​

Perform the multiplication first:
15 × 14 = 210

Then divide by 2:
2 210 ​ = 105


Therefore, there are 105 handshakes when 15 people each shake hands with one another. ;

Answered by JessicaJessy | 2025-07-21