Competition problem — Combinatorics

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Combinatorics Difficulty 1.9 Junior Find the answer

Let function $f: \{1, 2, 3\} \rightarrow \{1, 2, 3\}$ , then the number of functions $f(x)$ that satisfy "if $x_1 \neq x_2$ , then $f(x_1) \neq f(x_2)$ " is

Pick one

Solution

The functions $f(x)$ that satisfy "if $x_1 \neq x_2$ , then $f(x_1) \neq f(x_2)$ " are bijections.
The total number of such functions is $A_3^3 = 3 \times 2 \times 1 = 6$ ,
Therefore, the correct answer is $\boxed{D}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.