Functions
Bijective Functions
JEE Main 2021
Grade 12
Question:
Let $A = \{0, 1, 2, 3, 4, 5, 6, 7\}$. Find the number of bijective functions $f : A \to A$ such that $f(1) + f(2) + f(3) = 3$.
Step-by-Step Solution
Key Concept: List all ordered triples of distinct values from $A$ that sum to $3$. There is exactly one such set of values $\{0, 1, 2\}$. Then count the permutations of the remaining 5 elements.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 720