It was found at a certain dinner meeting that after every member had s

1.	It was found at a certain dinner meeting that after every member had shaken hand with every other members, 45 handshakes were interchanged. How many members were present at the metting?
Answer» et n be the member of person present in the meeting. The total number of handshakes is same as the number of ways of selecting 2 persons from among n persons. The total number of handshakes = nC₁ = 45 ⇒ \(\frac{n(n-1)}{1 \times 2}\) = 45 ⇒ n² – n – 90 = 0 ⇒ (n – 10)(n + 9) = 0 ⇒ n = 10, -9 n = 10 is acceptable.

It was found at a certain dinner meeting that after every member had shaken hand with every other members, 45 handshakes were interchanged. How many members were present at the metting?

Answer»

et n be the member of person present in the meeting. The total number of handshakes is same as the number of ways of selecting 2 persons from among n persons.

The total number of handshakes = nC₁ = 45

⇒ \(\frac{n(n-1)}{1 \times 2}\) = 45

⇒ n² – n – 90 = 0

⇒ (n – 10)(n + 9) = 0

⇒ n = 10, -9

n = 10 is acceptable.

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It was found at a certain dinner meeting that after every member had shaken hand with every other members, 45 handshakes were interchanged. How many members were present at the metting?

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