Question

The total number of functions, f : {1, 2, 3, 4} $\rightarrow$ {1, 2, 3, 4, 5, 6} such that f(1) + f(2) = f(3), is equal to

• A. 60
• B. 90
• C. 108
• D. 126

Answer 1

Answer: (B)

90

Answer 2

Case 1: If f(3) = 3 then f(1) and f(2) take 1 OR 2
No. of ways = 2⋅6 = 12
Case 2: If f(3) = 5 then f(1) and f(2) take 2 OR 3
OR 1 and 4
No. of ways = 2⋅6⋅2 = 24
Case 3: If f(3) = 2 then f(1) = f(2) = 1
No. of ways = 6
Case 4: If f(3) = 4 then f(1) = f(2) = 2
No. of ways = 6
OR f(1) and f(2) take 1 and 3
No. of ways = 12
Case 5: If f(3) = 6 then f(1) = f(2) = 3 ⇒ 6 ways
OR f(1) and f(2) take 1 and 5 ⇒ 12 ways
OR f(2) and f(1) take 2 and 4 ⇒ 12 ways