Suppose |A| = n, and let F = {f|f is a one-to-one, onto function from I, to A}. Prove that F is finite, and |F | = n!. (Hint: Use induction on n.) Let L = {R| R is a total order on A}. Prove that F = n!. Five people are to sit in a row of five seats. In how many ways can they be seated? L, and therefore |L|

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A: This is a question on the properties of continuous function.

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A: Given that .The objective, if then prove that .

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A: The first step is to check whether that the function f is bijective.

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