Number Of Permutations

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Problem 5 (Number Of Permutations)

Given finite set $X$ with $n$ elements, how many permutations are there of $X$?

• Show that if $X=\{1\}$, then there is only one permutation of $X$.
• Show that if $X=\{1,2\}$, then there are two permutations of $X$. List them.
• Make a list of all permutations of $X=\{1,2,3\}$, and then of $X=\{1,2,3,4\}$. What pattern do you see?
• Make a conjecture about the number of permutation of $X$ if $|X|=n$. Then prove your conjecture.

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