Get Started With Combinatorics 3 – Parade
Alice gets tired of standing in lines and heads off to her job as a parade coordinator for the US Navy. Her boss insists that she finish planning the parade by this afternoon. "After all," he says, "there are only 7 participants in this parade. How many options are there, really?"
How many possible orderings of the 7 parade participants should Alice consider if she wants to examine them all?
The answer is 5040.
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We proceed in a similar manner to the last problem.
There are 7 options for the first participant.
There are 6 options for the second participant,
There are 5 options for the third participant,
There are 4 options for the fourth participant,
There are 3 options for the fifth participant,
There are 2 options for the sixth participant,
There are 1 options for the seventh participant,
Hence, there are 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5 0 4 0 possible orders.