At d end of business meeting 10 people Present shake hands with each other once. How many handshakes will be there all together?
Answers
Answer :
There will be a total of 45 handshakes together .
Explaination :
10 people had attended the meeting .
They all shake hands with each other only one .
Here , ' only once ' is the keyword .
So, if one person shakes hands with 9 people , the next person will have only 8 people left with to shake hands and so on .
This is the pattern .
So, the total number of handshakes becomes :
=> 1 + 2 + ...... + 9
=> ( 9 × 10 )/2
=> 45 handshakes .
However , If the question is generalised for n people the number of handshakes will become n(n-1)/2 .
This is the required answer.
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Step-by-step explanation:
A can shake hands with B,C,D,E,F,G,H,I,J that is 9 persons.
Similarly B can shake hands with 8 people (As A has already shook hands with B, there is no need for B to shake hands with A again ).
C with 7…. D with 6…. E with 5…. F with 4…. G with 3…. H with 2 and I with 1(i.e. J).
Total handshakes = 9+8+7+6+5+4+3+2+1 = 45.
hope it helps !!!