Question

please tell me if this answer is correct

Answer 1

yeah !!!!
both are correct .
if you about npr = n!/(n -r)!
use this ,

(1) np5 = 42 np3
n!/( n -5)! = 42 n!/( n -3)!

n( n-1)(n-2)(n-3)(n-4)(n-5)!/(n-5)! = 42 n(n-1)(n-2)(n-3)!/(n-3)!

(n -3)(n -4) =42

n² -7n +12 = 42

n² -7n = 30

n² -10n +3n -30 = 0

n = 10 and n = -3
but n > 4 so, n = 10

(2) np4/(n-1)p4 = 5/3

{n(n-1)(n-2)(n-3)(n-4)!/(n-4)!}/(n-1)(n-2)(n-3)(n-4)(n-5)!/(n-1-4)!= 5/3

n( n -1)(n -2)(n-3)/(n-1)(n-2)(n-3)(n-4)= 5/3

3n = 5(n -4)

3n = 5n -20

-2n = -20

n = 10