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There are 20 people in a party. If every person shakes hand with every other person, what is the total number of handshakes?

Question

There are 20 people in a party. If every person shakes hands with every other person, what is the total number of handshakes?

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Solution

Sure, here is the step by step solution:

  1. We know that every person shakes hands with every other person. So, if there are 20 people, each person shakes hands with 19 other people.

  2. However, this counts every handshake twice (person A shaking hands with person B is the same as person B shaking hands with person A).

  3. So, we need to divide the total by 2 to avoid double counting.

Here is the calculation:

  1. Total handshakes if each person shakes hands with all others = 20 * 19 = 380
  2. But this counts every handshake twice, so we divide by 2: 380 / 2 = 190

So, there are 190 handshakes in total.

This problem has been solved

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