Question

If C(30, n - 3) = C(30, n + 3) then what is n equal to?
1. 10
2. 12
3. 15
4. 20

Answer 1

Correct Answer - Option 3 : 15

Concept:

ⁿC_x = ⁿC_y, then x = y or x + y = n

Calculation:

Given 

C(30, n - 3) = C(30, n + 3)

³⁰C_{n - 3} = ³⁰C_{n + 3}

n - 3 + n + 3 = 30

2n = 30

n = 15

Combination Formula

Let n and r are integer such that 0 ≤ r ≤ n, then

ⁿC_r = \(\rm \frac{n!}{r! (n -r)!}\)

ⁿP_r = ⁿC_r r!

ⁿC_{n - r} = ⁿC_r

ⁿC_r + ⁿC_{r - 1} = ^{n + 1}C_r

n ^{n - 1}C_{r - 1} = (n - r + 1) ⁿC_{r - 1}