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45
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avatar+39 

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

 Sep 20, 2020
 #1
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+1

 

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         

.

 Sep 20, 2020
 #2
avatar+27695 
+1

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

 Sep 20, 2020

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