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There are six people in a room each person shakes hands with another person once until they all shake hands fifteen handshakes occur Explain how the fifteen handshakes resulted?

Updated: 4/28/2022

Wiki User

15y ago

Start out with small cases and you will see the pattern. At that point, you might even guess what the formula is. So let's ay the room has only A and B---two people. there is one handshake

(A with B). Three people (A, B, and C), there are three handshakes

(A with B and C; B with C). Now, let's try four people (A, B, C, and D), there are six handshakes

(A with B, C, and D; B with C and D; C with D). So if we have n+1 people, the number of handshakes is the sum of the first n numbers. This is n(n+1)/2 So for 6 people it is the sum of the first 5 numbers, which is 1+2+3+4+5=15 or 5x6/2=30/2=15 Another way to think of this, if you have done some combinatorics, is for 6 people, in how many ways can you pick two. This is 6C2 or 6x5/2= 15

Wiki User

15y ago

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Q: There are six people in a room each person shakes hands with another person once until they all shake hands fifteen handshakes occur Explain how the fifteen handshakes resulted?
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