Permutations & Combinations
3-Digit Numbers with Digit Sum 14
nta_pyq_2024_apr
Grade 11
Question:
The number of integers, between 100 and 1000 having the sum of their digits equals to 14, is
Step-by-Step Solution
Key Concept: 3-digit number $abc$ with $a+b+c=14$, $a\geq1$, $b,c\in\{0,\ldots,9\}$. Three cases: (i) all digits distinct, (ii) exactly two same, (iii) all same.
All distinct: $8\times3!=48$. Two same: 14. All same: 0. Total $=70$.
Correct Answer: 70