Permutations & Combinations
Strictly Increasing f with f(i)≠i
nta_pyq_2026_jan
Grade 11
Question:
The number of strictly increasing functions $f$ from the set $\{1,2,3,4,5,6\}$ to the set $\{1,2,3,\ldots,9\}$ such that $f(i)\neq i$ for $1\leq i\leq6$, is equal to:
Step-by-Step Solution
Key Concept: Strictly increasing $f$ means $f$ is determined by choosing 6 values from $\{1,\ldots,9\}$. Condition $f(i)\geq i+1$ for all $i$. Let $h(i)=f(i)-i\geq1$; $h$ is non-decreasing and $h(i)\in\{1,2,3\}$.
28 functions.
Correct Answer: 4