10 people attend a party. During the party everyone shakes hands with everyone else. How many handshakes take place at the party?

blobfishesarecool Sep 20, 2020

#1**+2 **

*10 people attend a party. During the party everyone shakes hands with everyone else. How many handshakes take place at the party?*

What would this be, combinations or permutations.

Combinations would be how many ways could you group 2 different people.

Permutations would be the same, except it would count A & B and B & A as two different handshakes, which is wrong.

So, it's combinations.

n!

The formula for combinations of n things, taken r at a time is: ——————

( r! (n – r)! )

10! 3,626,800

Just plug in the numbers and get ———— = ——————

(2!) (8!) (2) (40,320)

Break out the old calculator to do the arithmetic and obtain **45**

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Guest Sep 20, 2020

#2**+2 **

10 people must shake hands with 9 other people 10 x 9 = 90

BUT each handshake invilves TWO peole...so divide by 2 90/ 2 = 45 handshakes

ElectricPavlov Sep 20, 2020