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Question

Mathematics Question on permutations and combinations

The range of the function f(x)=7−xPx−3f\left(x\right) = ^{7-x}P_{x-3} is

A

{1, 2, 3}

B

{1, 2, 3, 4, 5}

C

{1, 2, 3, 4}

D

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

Answer

{1, 2, 3}

Explanation

Solution

f(x)= 7−xPx−3f\left(x\right) = \,^{7-x}P_{x-3} 7−x≥0?x≤77 - x \ge 0 \quad? \quad x \le 7 x−3≥0?x≥3,x - 3 \ge 0 \quad ?\quad x \ge 3 , and 7−x≥x−3?x≤57 - x \ge x - 3 \quad ? \quad x \le 5 ?3≤x≤5?x=3,4,5?? 3 \le x \le 5? x = 3, 4, 5 ? Range is 1,2,3.1, 2, 3.