Total 6-Digit Numbers
To find the total number of 6-digit numbers where the sum of the digits is divisible by 5, we need to consider the properties of digits and their arrangements.
Range of 6-Digit Numbers
- The smallest 6-digit number is 100000.
- The largest 6-digit number is 999999.
Counting Total 6-Digit Numbers
- The total number of 6-digit numbers can be calculated as follows:
- Total = 999999 - 100000 + 1 = 900000.
Sum of Digits Divisibility by 5
- A number's digit sum can yield residues 0, 1, 2, 3, or 4 when divided by 5.
- By the principle of uniform distribution, we can expect that the sums will be evenly distributed among these residues.
Dividing by 5
- Since there are 5 possible residues, the expected count of 6-digit numbers where the sum of digits is divisible by 5 (i.e., residue 0) is approximately:
- Total 6-digit numbers / 5 = 900000 / 5 = 180000.
Conclusion
- Therefore, the total number of 6-digit numbers in which the sum of the digits is divisible by 5 is approximately 180000.
This calculation uses assumptions of uniform distribution, which is generally effective for large sets of numbers.