Question

If P(n-1,3):P(n,3) = 1:9, find n.
4
6
9
7
8

Answer 1

P(n-1,3)/p(n,3)=1/9.
N=9

Answer 2

AnswEr:

We have,

$\qquad \sf \: P(n - 1, 3) \: \colon \: P(n,4) = 1 \: \colon \: 9 \\ \\ \hookrightarrow \sf \frac{P(n - 1,3)}{P(n,4)} = \frac{1}{9} \\ \\ \hookrightarrow \sf \frac{(n - 1)!}{(n - 1 - 3 )! \div n ! \div (n - 4)!} = \frac{1}{9} \\ \\ \hookrightarrow \sf \frac{(n - 1)!}{(n - 4)!} \times \frac{(n - 4)!}{n!} = \frac{1}{9} \\ \\ \hookrightarrow \sf \frac{(n - 1)!}{n!} = \frac{1}{9} \\ \\ \hookrightarrow \sf \frac{(n - 1)!}{n(n - 1)!} = \frac{1}{9} \\ \\ \hookrightarrow \sf \: n = 9 \\ \\ \therefore \sf \: n = 9$

Therefore, value of n will be 9