First slide

Permutations

Question

The range of the function $f (x) =^{15 - x} P_{x - 8}$ is

Moderate

A

{1, 6, 20, 24}
B

{1, 6, 10, 15}
C

{1, 4, 11, 15}
D

{1, 8, 11, 19}

Solution

We must have $15 - x \geq 1$ and $x - 8 \geq 0$ and
$15 - x \geq x - 8 \Rightarrow 8 \leq x \leq 11$ Now,
$\begin{array}{l} f (8) =^{7} P_{0} = 1, f (9) =^{6} P_{1} = 6 \\ f (10) =^{5} P_{2} = 20, f (11) =^{4} P_{3} = 24, \end{array}$
Thus, range of $f$ is {1, 6, 20, 24}.

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