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Question

# Use an organized list, a tree diagram, or the fundamental counting principle to find the number of permutations. the number of ways 6 shirts can be arranged in a closet

Solution

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The fundamental counting principle is the easiest to use to find the number of permutations in this case.

By the $\textbf{Fundamental Counting Principle:}$ If an event can occur in $m$ ways and a second event can occur in $n$ ways, then the total number of possible ways that these events occur together is equal to $m\cdot n$. This can be extended to more than 2 events.

Each time a shirt is placed in the closet, the number of shirts (choices) decreases by 1 so the number of possible permutations is:

$6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=\color{#c34632}720$

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