The total number of functions, f : {1, 2, 3, 4} • {1, 2, 3, 4, 5, 6

1.	The total number of functions, f : {1, 2, 3, 4} • {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» Correct option is (B) 90 A = {1, 2, 3, 4} B = {1, 2, 3, 4, 5, 6} Here f(3) can be 2, 3, 4, 5, 6 f(3) = 2, (f(1), f(2)) → (1,1) → 6 cases f(3) = 3, (f(1), f(2)) → (1,2), (2,1) → 2 × 6 = 12 cases f(3) = 4, (f(1), f(2)) → (1,3), (3,1), (2,2) → 3 × 6 = 18 cases f(3) = 5, (f(1), f(2)) → (1,4), (4,1), (2,3), (3,2) → 4 × 6 = 24 cases f(3) = 6, (f(1), f(2)) → (1,5),(5,1),(2,4),(4,2),(3,3) → 5 × 6 = 30 cases

The total number of functions, f : {1, 2, 3, 4} • {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»

Correct option is (B) 90

A = {1, 2, 3, 4}

B = {1, 2, 3, 4, 5, 6}

Here f(3) can be 2, 3, 4, 5, 6

f(3) = 2, (f(1), f(2)) → (1,1) → 6 cases

f(3) = 3, (f(1), f(2)) → (1,2), (2,1)

→ 2 × 6 = 12 cases

f(3) = 4, (f(1), f(2)) → (1,3), (3,1), (2,2)

→ 3 × 6 = 18 cases

f(3) = 5, (f(1), f(2)) → (1,4), (4,1), (2,3), (3,2)

→ 4 × 6 = 24 cases

f(3) = 6, (f(1), f(2)) → (1,5),(5,1),(2,4),(4,2),(3,3)

→ 5 × 6 = 30 cases

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The total number of functions, f : {1, 2, 3, 4} • {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

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