IPMAT Indore 2025
Modern Math
Permutation & Combination
Easy
The number of integers greater than 5000 and divisible by 5 that can be formed with the digits 1, 3, 5, 7, 8, 9 where no digit is repeated is
The number of integers greater than 5000 and divisible by 5 that can be formed with the digits 1, 3, 5, 7, 8, 9 where no digit is repeated is
✅ Correct Option: 1
We need to find integers that are > 5000, divisible by 5, using only digits 1, 3, 5, 7, 8, 9 without repetition.
First, for a number to be divisible by 5, its last digit must be either 0 or 5.Since 0 is not in our set of available digits, the only option is to use 5 as the last digit.
Since we need numbers greater than 5000, they must have at least 4 digits. The maximum possible length is 6 digits (as we have 6 available digits).
4-digit numbers: - Last digit must be 5 - First digit must be to ensure the number is > 5000 (We can't use 5 again) - From our available digits, only 7, 8, 9 are - We have 3 choices for the first digit (7, 8, 9) - We have 4 choices for the second digit (all except first and 5) - We have 3 choices for the third digit (all except first, second, and 5)Number of 4-digit numbers =
5-digit numbers: - Last digit must be 5 - First digit can be any of the 5 digits except 5 - Remaining positions filled with remaining digitsNumber of 5-digit numbers =
6-digit numbers: - Last digit must be 5 - First digit can be any of the 5 digits except 5 - Remaining positions filled with remaining digitsNumber of 6-digit numbers =
Total number of valid integers = Therefore, there are 276 integers greater than 5000 and divisible by 5 that can be formed with the given digits without repetition.
First, for a number to be divisible by 5, its last digit must be either 0 or 5.Since 0 is not in our set of available digits, the only option is to use 5 as the last digit.
Since we need numbers greater than 5000, they must have at least 4 digits. The maximum possible length is 6 digits (as we have 6 available digits).
4-digit numbers: - Last digit must be 5 - First digit must be to ensure the number is > 5000 (We can't use 5 again) - From our available digits, only 7, 8, 9 are - We have 3 choices for the first digit (7, 8, 9) - We have 4 choices for the second digit (all except first and 5) - We have 3 choices for the third digit (all except first, second, and 5)Number of 4-digit numbers =
5-digit numbers: - Last digit must be 5 - First digit can be any of the 5 digits except 5 - Remaining positions filled with remaining digitsNumber of 5-digit numbers =
6-digit numbers: - Last digit must be 5 - First digit can be any of the 5 digits except 5 - Remaining positions filled with remaining digitsNumber of 6-digit numbers =
Total number of valid integers = Therefore, there are 276 integers greater than 5000 and divisible by 5 that can be formed with the given digits without repetition.
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