inductive reasoning: seven people shake hands w/ each other

missalissa

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Seven people meet and shake hands with one another. Using inductive reasoning, write a formula for the number of handshakes if the number of poeple is n.

So far I have (n-1)[n- ] but I'm not sure if that's right or not.

Any help is appreciated! Thank you!
 
\(\displaystyle \L\\\frac{n(n-1)}{2}\)

or

\(\displaystyle \L\\C(n,2)\)
 
missalissa said:
So far I have (n-1)[n- ] but I'm not sure if that's right or not.
How did you get that? What was your reasoning?

Please reply with full details. Thank you.

Eliz.
 
Re: inductive reasoning: seven people shake hands w/ each ot

missalissa said:
Seven people meet and shake hands with one another. Using inductive reasoning, write a formula for the number of handshakes if the number of poeple is n.

So far I have (n-1)[n- ] but I'm not sure if that's right or not.

Any help is appreciated! Thank you
Person 1 shakes the hand of 6 people.
Person 2 shakes the hand of 5 peop;e, already having shaked the hand of person 1.
Person 3 shakes the hand of 4 people, already having shaken the hands of persos 1 and 2.

Carrying this to its logical conclusion, the number of hand shakes is 6 + 5 + 4 + 3 + 2 + 1 = 21.

This is simply the sum of the consecutive numbers from 1 to (n - 1), n being the number of people involved.

The formula for the sum of a set of consecutive numbers starting with one is S = n(n + 1)/2.

Since you want the formula in terms of the number of people involved, we make the following adjustment to the formula.

The numer of handshakes of n people is S = (n - 1)((n - 1 + 1))/2 = (n(n - 1)/2.

In your case of 7 people, S = 7(7 - 1)/2 = 21.
 
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