If at the end of a certain meeting,everyone h | vedclass

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Question

(A) Let $n$ be the number of members in the meeting.Since every person shakes hands with every other person exactly once,the total number of handshake

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(A) Let $n$ be the number of members in the meeting.Since every person shakes hands with every other person exactly once,the total number of handshakes is given by the combination formula ${}^{n}C_{2}$.Given that the total number of handshakes is $45$,we have:${}^{n}C_{2} = 45$$\frac{n(n-1)}{2} = 45$$n(n-1) = 90$$n^2 - n - 90 = 0$$(n - 10)(n + 9) = 0$Since the number of members $n$ must be positive,we have $n = 10$.Therefore,the number of members present at the meeting is $10$.

If at the end of a certain meeting,everyone had shaken hands with everyone else,and it was found that $45$ handshakes were exchanged,then the number of members present at the meeting is:

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