Happy new year

Let there are n n peoples in a new year party. Each person greets one another "HAPPY NEW YEAR", and there is no replies such as "same to you".

Determine the number of times "HAPPY NEW YEAR", is said.

n n ( n 2 ) \binom n2 1 2 ( n 2 ) \frac12 \binom n2 ( n 2 ) 2 \binom n2 ^2 2 ( n 2 ) 2 \binom n2

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1 solution

Vishakh Vasu
Dec 31, 2016

For n peoples no. of combinations of two persons at a time will be (n¦2) Now each person says "HAPPY NEW YEAR", so two times "HAPPY NEW YEAR" is said per combination. Therefore, total no. of times "HAPPY NEW YEAR" is said = 2 x (n¦2).

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