Given:
P (9, r) = 3024
By using the formula,
P (n, r) =\( \dfrac{ n!}{r!(n – r)!}\)
P (9, r) = \( \dfrac{ 9!}{r!(9 – r)!}\)
So, from the question,
P (9, r) = 3024
Substituting the obtained values in above expression we get,
\( \dfrac{ 9!}{r!(9 – r)!}\)= 3024
\( \dfrac{1}{(9 – r)!}= \dfrac{3024}{9!}\)
= \( \dfrac{3024}{(9×8×7×6×5×4×3×2×1)}\)
= \(\dfrac{ 1}{5!}\)
(9 – r)! = 5!
9 – r = 5
-r = 5 – 9
-r = -4
The value of r is 4.
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