Question -
Answer -
Given:
n + 2C8: n – 2P4 =57: 16
n + 2C8 / n – 2P4 =57 / 16
Let us use theformula,
nCr = n!/r!(n – r)!
[(n+2)!(n-6)!] / [(n-6)! (n-2)! 8!] = 57/16
(n+2) (n+1) (n) (n-1)/ 8! = 57/16
(n+2) (n+1) (n) (n-1)= (57×8!) / 16
(n+2) (n+1) (n) (n-1)= [19×3 × 8×7×6×5×4×3×2×1]/16
(n + 2) (n + 1) (n) (n– 1) = 21 × 20 × 19 × 18
Equating thecorresponding terms on both sides we get,
n = 19
∴ The value of nis 19.