Question

n+2 c 8:n-2 c 4=57:16

Answer 1

(n+2)C8 : (n - 2)P4 = 57 :16. (n+2)C8 / (n - 2)P4 = 57 / 16. ( n + 2 )! ( n - 6)! / ( n - 6)! 8! ( n - 2) ! = 57 / 16 ( n + 2 )! / 8! ( n - 2) ! = 57 / 16. ( n + 2)( n + 1)n ( n - 1) (n - 2)! / 8! ( n - 2) ! = 57 / 16. ( n + 2)( n + 1)n ( n - 1) = (57 x 8! ) / 16 ( n + 2)( n + 1)n ( n - 1) = 21 x 20 x 19 x 18.

∴ n = 19