Permutations & Combinations
Counting numbers in range divisible by 3 or 11
nta_pyq_2023_jan
Grade 11
Question:
Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11, is equal to _____.
Step-by-Step Solution
Key Concept: Use inclusion-exclusion for 4-digit numbers [1000, 2800] divisible by 3 or 11.
n(3) in [1000,2800]=600, n(11) in [1000,2800]=164, n(33) in [1000,2800]=54. Total = 600+164−54 = 710.
Correct Answer: 710