Question

The number of three-digit number abc formed such that a ≠ b ≠ c and 2b = a + c is 

(A)  12 

(B)  256 

(C)  32 

(D)  36

Answer 1

Correct option  (D) 36

2b = a + c ⇒ either both odd or both even

when both odd, the number of ways = ⁵C₂ x 2

when both even, the number of ways = ⁴C₂ x 2 + ⁴C₁

Therefore, the total numbers of ways = 36.