Question

nP4 = 12 nP2 Then find n.

Answer 1

Hi there here is your answer.....

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Answer 2

Answer:

n=6

Step-by-step explanation:

Given : $_nP_4= 12\times _nP_2$

To Find: n

Solution:

Formula : $_nP_r= \frac{n!}{(n-r)!}$

So,   $_nP_4= 12\times _nP_2$

Using formula            

$\frac{n!}{(n-4)!}= 12\times \frac{n!}{(n-2)!}$

$\frac{1}{(n-4)!}= 12\times \frac{1}{(n-2)!}$

$\frac{1}{(n-4)!}= 12\times \frac{1}{(n-2)(n-3)(n-4)!}$

$1 = 12\times \frac{1}{(n-2)(n-3)}$

$(n-2)(n-3) = 12$

$n^2-2n-3n+6 = 12$

$n^2-5n+6-12=0$

$n^2-5n-6=0$

$n^2-6n+n-6=0$

$n(n-6)+1(n-6)=0$

$(n+1)(n-6)=0$

$n = -1,n = 6$

Since n cannot be negative .

So, n = 6