Sets, Relations & Functions
Counting One-One Functions with Constraint
nta_pyq_2024_apr
Grade 11
Question:
Let $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$. Then the total number of one-one maps $f:A\to B$, such that $f(1)+f(3)=14$, is:
Step-by-Step Solution
Key Concept: Pairs from $B$ summing to 14: $(2,12)$ and $(4,10)$. For each pair, 2 assignments for $f(1),f(3)$. Remaining 3 elements of $A$ map to remaining 5 elements: $5\times4\times3=60$ ways.
2 pairs $\times$ 2 orderings $\times$ $P(5,3)=240$.
Correct Answer: 2