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# Discrete Mathematics Warmups

If there are only a handful of objects, then you can count them with a moment's thought, but the techniques of combinatorics can extend to quickly and efficiently tabulating astronomical quantities.

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If two fair coins are tossed simultaneously, what is the probability that exactly one head appears?

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Hassan Raza**

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In a business meeting, a total of 45 handshakes occurred. How many people were at the meeting?

Assume that each person shakes hands with each other person exactly once.

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Aronas Nuresi**

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How many triangles are there in the above image?

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Calvin Lin**

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Matthew Tam**

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If someone painted the outside of a \( 5 \times 5 \times 5 \) cube made out of \( 1 \times 1 \times 1 \) unit cubes, how many of the unit cubes would have paint on exactly 3 sides?

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Arron Kau**

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