The Friendly Crowd

Probability Level 2

1,000 people are present in a room. If each person were to shake hands with each other, what would be the total number of handshakes?


The answer is 499500.

William Lockhart by William Lockhart , 29, Canada

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3 solutions

Godwin Tom George
Sep 22, 2014

It's like choosing 1000 people as a group of 2 ,(without repetition). It can be done in

1000C2 ways=499500

1 Helpful 0 Interesting 0 Brilliant 0 Confused
William Lockhart
Sep 22, 2014

Person #1 would shake hands with the remaining 999 people. Person #2 has already shaken hands with person #1, so is only left to shake hands with the remaining 998 people, and so on. The sum of all handshakes is the equal to the sum of all natural numbers up to 999.

s=1+2+3+...+997+998+999

The sum can be calculated using the following formula...

s=n(n+1)/2

s=999(999+1)/2

s=999(1000)/2

s=999000/2

s=499500

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Sunil Pradhan
Oct 31, 2014

Total number of shakes hands = n(n – 1)/2

= 1000 × 999/2 = 499500

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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