Question

Has anyone have It was simran's first day at school that teacher suggested that it would be a good idea for each child to meet every other child in the class. the teacher said, "when you meet me shake hands and introduce yourself by name. " if there were seven children in the class how many total handshakes were there?

Answer 1

There are total 7 children

See for first child there would be 6 children available to handshake

Now for Second child there would be 5 children available as child has already shaken hand with first child

For 3 rd child 6 children available as child already has shaken hand with 2 children

So on...

for 6 th children only 1 handshake as 5 handshake already done

So

6 +5+4+3+2+1 = 21 total handshakes

Or

As there are 7 children

here to have handshake 2 needs to be selected

So 7C2 would give no of ways 2 students can be selected out of 7

= 7! /2! (7-2)!

= 7!/2!(5!)

= 7× 6× 5!/ 2 × 5!

= 7× 6/2 .

= 7× 3

= 21

Answer 2

Answer:

Step-by-step explanation:

We know that for a handshake,we need two people.

We need to select two people from a group of 7.

Applying the concept of combinations,Number of ways of selecting two children out of 7=7C2= 7!/(2! * 5!)=21

Hence, number of handshakes=21

Hope you understood