a class has 10 children .on the first day of the school the teacher asked each child to shake hands with every other child in the class.how many total handshakes were there?
answer is: 45 but how???
Answers
Answered by
7
8Half of them should not be considered since the other half of students already shook hands and thus it would be 5×9=45 since they did not shake hands with themselves
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1246:
i dint understood
can you explain
see, if you and your friend have to shake hands then your fnd wont have to shake as you already have shook hands with him
Similarly, here, if 10 students are there , first five students shook hands with the other five, so, the other half didn't have to, understood?
what???
Answered by
7
If all of these pairs shake hands, each person in the room will shake hands with EVERY OTHER PERSON in the room. The result will be 9 HANDSHAKES PER PERSON.
The total number of pairs that can be formed from 10 people
= 10C2
= (10x9)/1x2
= 90/2
=45
Another way of considering it is that each person has a total of n-1 handshakes, and there are n people, so there would be (n-1)(n) handshakes, but this includes each handshake twice (1 and 2, 2 and 1) so dividing by 2 gives the correct answer.
So, total handshakes = 10x9/2 = 45
The total number of pairs that can be formed from 10 people
= 10C2
= (10x9)/1x2
= 90/2
=45
Another way of considering it is that each person has a total of n-1 handshakes, and there are n people, so there would be (n-1)(n) handshakes, but this includes each handshake twice (1 and 2, 2 and 1) so dividing by 2 gives the correct answer.
So, total handshakes = 10x9/2 = 45
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