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Functions: Number Functions Range Contains Exactly Elements

JEE Maths question with a full step-by-step solution.

Question
If n(A)=4n(A) = 4, n(B)=5n(B) = 5 and the number of functions from AA to BB such that range contains exactly 3 elements is kk, then k/60k/60 is.
Solution
Answer: 6
Solution Step 1: Choose the 3 elements in the range
5C3=10{}^5C_3 = 10
 Step 2: Count onto functions from AA (4 elements) to exactly 3 elements By inclusion-exclusion:
34−(31)⋅24+(32)⋅14=81−48+3=363^4 - \binom{3}{1}\cdot 2^4 + \binom{3}{2}\cdot 1^4 = 81-48+3 = 36
 Step 3: Compute k/60k/60
k=10×36=360  ⟹  k60=36060=6k = 10 \times 36 = 360 \implies \frac{k}{60} = \frac{360}{60} = 6
 Answer: 6
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