Permutations & Combinations
Serial number of a number in ascending order with repetition
nta_pyq_2023_jan
Grade 11
Question:
Let 5 digit numbers be constructed using the digits 0, 2, 3, 4, 7, 9 with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is
Step-by-Step Solution
Key Concept: Count all 5-digit numbers (first digit $\neq$ 0) less than 42923 using digits {0,2,3,4,7,9} with repetition.
Numbers starting with 2,3 (each 6⁴=1296), starting with 40,42(0 only) groups are counted systematically. Total numbers before 42923 = 2$\times$1296+216+36+36+36+36+36+6+1+1+1 = 2996. Serial number = 2997.
Correct Answer: 2997