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Question: If \(n + 2C_{8}:^{n - 2}P_{4} = 57\):16, then n is equal to...

If n+2C8:n2P4=57n + 2C_{8}:^{n - 2}P_{4} = 57:16, then n is equal to

A

19

B

18

C

17

D

20

Answer

19

Explanation

Solution

Given

n+2n+286mu86mux6mun24n26mu=6mu5716\frac{\angle n + 2}{\angle n + 2 - 8\mspace{6mu}\angle 8}\mspace{6mu} x\mspace{6mu}\frac{\angle n - 2 - 4}{\angle n - 2}\mspace{6mu} = \mspace{6mu}\frac{57}{16}

n+2n26mu=6mu86mux6mu5716\frac{\angle n + 2}{\angle n - 2}\mspace{6mu} = \mspace{6mu}\angle 8\mspace{6mu} x\mspace{6mu}\frac{57}{16}

⇒ (n+2) (n+1) n (n – 1)

= 8x7x6x5x4x3x2x5716\frac{8x7x6x5x4x3x2x57}{16}

= 7 x 6 x 5 x 4 x 3 x 19 x 3

= (7 x3) (5 x 4) (19) (6 x 3)

= 21 x 20 x 19 x 18

⇒ n = 19 (By inspection)