By using the formula,
P (n, r) = \( \dfrac{ n!}{r!(n – r)!}\)
P (n – 1, 3) = \(\dfrac{ (n – 1)! }{ (n – 1 – 3)!}\)
=\(\dfrac{ (n – 1)! }{ (n – 4)!}\)
P (n, 4) = \( \dfrac{ n!}{r!(n – 4)!}\)
So, from the question,
\(\dfrac{ P (n – 1, 3)}{ P (n, 4)} = \dfrac{1 }{ 9}\)
Substituting the obtained values in above expression we get,
\(\dfrac{ n!}{r!(n – r)!} = \dfrac{1}{9}\)
\( \dfrac{1}{n}= \dfrac{1}{9}\)
n = 9
The value of n is 9.
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