JEE Main 2023 (Online) 31st January Morning ShiftQuestion 1
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 ______.
Permutation and Combination
Answer$2997$
Solution
Count numbers up to $42923$: first digit $2$ or $3$: $2\cdot6^4=2592$; $40\ast\ast\ast$: $216$; $42$ with third digit $0,2,3,4,7$: $5\cdot36=180$; $4290\ast$: $6$; $4292\ast\le42923$: $3$. Serial number $2997$.