Question

If each student meets their classmate with a handshake and there are 20 students how many handshakes will happen

Answer 1

Answer:

total number of persons is 20 , so every person shakes hands with 19 persons.. It then mean that, there are 20×19=380 handshakes

Answer 2

Answer:

190 handshakes will take place.

Explanation:

There are two ways of solving this:

First method:

There are 20 students in the class. To find the number of handshakes is like finding the number of ways in which 2 objects can be drawn out of 20. We need to find how many pairs of two boys are possible out of 20 boys.

This is given by:

20C2 = 20!/[(20-2)!*2!}

          = 20!/(18! * 2!)

          = (20*19)/2

          = 190

Second method:

Consider the first boy. He will shake hands with 19 boys.

Consider the second boy. He will shake hands with 18 boys because he has already shaken hands with the first boy.

Similarly, the third boy will shake hands with 17 boys and so on.

Hence, we need to find the sum of: 19, 18, 17, ......1

This can be thought of as an AP with

first term = 1

common difference = 1

no. of terms = 19

We know that sum of first n terms of an AP with first term "a" and common difference "d" is given by:

$\frac{n}{2} [2a + (n-1)d]$

Substituting a = 1, d = 1, n = 19, we get:

Sum = (19/2)*(2 + 18)

        = (19*20)/2 = 190

Answer: A total of 190 handshakes will take place