Question

Find the value of x such that: ${}^7{C}_{x-1}{+}^7{C}_x{=}^8{C}_{x+2}$

• A. 2
• B. 3
• C. 4
• D. 5
• E. 6

Answer 1

The correct option is B 3

Soln: We have ${}^n{C}_{r-1}+n{C}_r{=}^{n+1}{C}_r$
${}^7{C}_{x-1}{+}^7{C}_x{=}^8{C}_x$

${}^8{C}_x{=}^8{C}_{x+2}{=}^8{C}_{(8-x-2)}$

Either x = x + 2 or x + 2 = (8 - x - 2)

But $x\ne x+2$

2x + 2 = 8

x = 3

Hence option (b)

Alternatively, go from answer options.