3. Ten people met for the first time at a party. If they will shake hands once at each other. how many handshakes will be made?
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Answer:
If 10 people meet and shakes hand with each other. First person will shakes hand with other 9, second person had already shakes hand with 1st person and shakes hand with other 8, third………..
So, the total no. of hand shakes= 9+8+7+6+5+4+3+2+1=45 shakes
The other way to calculate this is by the formula n(n+1)/2
where n is the no. of shake hands by very first person and that is 9.
So, the total no. of hand shakes=9(9+1)/2
= 9(10)/2
=90/2
=45 shakes
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