Question:
If nP4 : nP5 = 1 : 2, then n =__________.
Solution:
${ }^{n} P_{4}:{ }^{n} P_{5}=1: 2$
i. e $\frac{{ }^{n} P_{4}}{{ }^{n} P_{5}}=\frac{1}{2}$
$\frac{n !}{(n-4) !} \times \frac{(n-5) !}{n !}=\frac{1}{2}$
$\frac{n !(n-5) !}{(n-4)(n-5) ! n !}=\frac{1}{2}$
$2=n-4$
i. e $n=6$
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