# SAT – Counting and Ordering

Q:  When 5 people met for dinner, each person shook hands with each other person once.  How many handshakes happened?

Explanation 1: Two people = a handshake.  This question is really ‘How many ways are there to choose 2 people from a total of 5, if the order is not important?’ It’s a combination question. Find the nCr function on your calculator. Type in 5 nCr 2. It’s 10. (There is a longer way to do it by hand, using the formula for nCr.)

Explanation 2: Person A shook hands with 4 people.  That’s  4 handshakes so far. Person B shook hands with 3 other people (his shake with A has already been counted). Person C shook hands with 2 other people.  Person D shook hands with 1 other person (E). Add: 4 + 3 + 2 + 1 = 10.

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