There are ten kids in a class. When any two meet, they shake their hands. Before the class starts, how many handshakes are there?

45 handshakes.

Step-by-step explanation:

We have 10 kids.

Let's count.

Kid 1, can meet other 9 kids, so here we have 9 handshakes.

Kid 2, he can meet other 9 kids, but he already handshaked kid 1, so here we only count 8 handshakes.

Kid 3, he can meet other 9 kids, but we already counted the handshake with kid 1 and kid 2, so from here we only count 7 handshakes.

You can see the pattern, the total number of handshakes will be:

H = 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1  = 45

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step-by-step explanation:

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