Question

if n-1p3:np4=1:9,find n

Answer 1

Answer:

Step-by-step explanation:

Hello ans is in the attachment below

Answer 2

Answer:

n = 9

Step-by-step explanation:

$^{n-1}P_{3} \: : \: ^{n}P_{4} = 1 \: : \: 9\\\\\\\implies \dfrac{(n-1)!}{(n-1-3)!} \div \dfrac{(n)!}{(n-4)!} = 1 \div 9\\\\\\\implies \dfrac{(n-1)! \times (n-4)!}{(n-4)! \times (n)!} = \dfrac{1}{9}\\\\\\\implies \dfrac{(n-1)!}{n(n-1)!} = \dfrac{1}{9}\\\\\\\implies \dfrac{1}{n} = \dfrac{1}{9}\\\\\\\implies n = 9\\\\\\\boxed{\boxed{\underline{\boxed{\bold{n = 9}}}}}$

Properties Used:

$1. \; ^nP_r = \dfrac{n!}{(n-r)!}$

And

$2. \; n! = n(n-1)!$