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 hand with every other person, what is the total number of handshakes?
Solution
Sure, here is the step by step solution:
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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.
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However, this counts every handshake twice (person A shaking hands with person B is the same as person B shaking hands with person A).
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So, we need to divide the total by 2 to avoid double counting.
Here is the calculation:
- Total handshakes if each person shakes hands with all others = 20 * 19 = 380
- But this counts every handshake twice, so we divide by 2: 380 / 2 = 190
So, there are 190 handshakes in total.
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