Permutations & Combinations
9-digit Numbers with AP Digits and Consecutive AP Constraint
nta_pyq_2023_apr
Grade 11
Question:
Digits $a,b,c$ in AP. 9-digit numbers using each thrice with at least one set of 3 consecutive digits in AP. How many such numbers?
Step-by-Step Solution
Key Concept: Total 9-digit arrangements of $a,a,a,b,b,b,c,c,c$: $\frac{9!}{3!3!3!}=1680$. Subtract those with NO 3 consecutive digits in AP.
1260 such numbers.
Correct Answer: 1260