Discussion
There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?
Answer: D
A handshake involves two people and the order does not matter, so the count is a combination.
\[ {}^{30}C_{2} = \frac{30 \times 29}{2} = 435 \]
Each of the 30 people shakes 29 hands, but that counts every handshake twice, hence the division by 2.
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