Class 11

Math

Algebra

Permutations and Combinations

Everybody in a function shakes hand with everybody else. The total number of handshakes are 45. Find the number of persons in the function.

We name the people as $1,2,3....,x−1,x$

Take person 1: He can shake hands with $(x−1)$ people.

Take person 2: He can shake hands with $(x−2)$ people.

......

Take person $x−1$: He can shake hands with 1 people.

Adding them together:

$(x−1)+(x−2)+...+1=4$

$2x(x−1) =45$

$x=10$

There were 10 people in the party.