Question

There are 60 athletes at a meeting. Theyeach shake hands with everyone else.How many handshakes were there?

Answer 1

1,770 handshakes

Explanation:

The number of athletes = 60.

Handshakes occur with 2 people at a time so we must count the number of possible unique pairings.

• Thus, first, each person shakes 59 people.

,

• But to get the number of unique handshakes, divide the result by 2.

Therefore, in general for pairs, the number of unique handshakes is determined using the formula:

`^nC_2=(n(n-1))/(2)`

When n=60

`\text{The number of handshakes}=(60(60-1))/(2)=30*59=1770`

There are 1,770 handshakes.