First slide

Permutations

Question

The range of the function $^{7 - x} P_{x - 3}$ is

Moderate

A

{1, 2, 3, 4}
B

{1, 2, 3, 4, 5, 6}
C

{1, 2, 3}
D

{1, 2, 3, 4, 5}

Solution

We must have $7 - x \geq 1, x - 3 \geq 0$ and $x - 3 \leq 7 - x$
$\Rightarrow x \leq 6, x \geq 3 and x \leq 5$
$∴ {Range of}^{7 - x} P_{x - 3} is \{^{4} P_{0},^{3} P_{1},^{2} P_{2}\} = {1, 3, 2}$

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