Question

P(n,4)=3024 can you give me answer​

Answer 1

Answer:

answer is on course book

Answer 2

Therefore n=9

Step-by-step explanation:

P(n,4)= 3024

$\Rightarrow ^nP_4=3024$

n!=1×2×3×4×.........×(n-1)×n.

n!=n(n-1)!

We know that

$^nP_r=\frac{n!}{(n-r)!}$

So,

$^nP_4=3024$

$\Rightarrow \frac{n!}{(n-4)!} =3024$

$\Rightarrow \frac{n(n-1)(n-2)(n-3)(n-4)!}{(n-4)!} =3024$               [applying   n!=n(n-1)!]

$\Rightarrow n(n-1)(n-2)(n-3)=3024$

Factor of 3024=2×2×2×2×3×3×3×7

                        =9×8×7×6

$\Rightarrow n(n-1)(n-2)(n-3)=9\times 8\times 7\times 6$

Therefore from the above equation it is clear that n=9