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Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are [2002]
  • a)
    312
  • b)
    3125
  • c)
    120
  • d)
    216
Correct answer is option 'D'. Can you explain this answer?
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Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 w...
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Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 w...
To find the total number of five-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, and 5 without repetition and are divisible by 3, we need to follow the following steps:

1. Understanding the Divisibility Rule of 3:
- A number is divisible by 3 if the sum of its digits is divisible by 3.

2. Counting the total number of digits:
- We have six digits (0, 1, 2, 3, 4, and 5) available to form a five-digit number without repetition.

3. Finding the sum of digits:
- The sum of digits from 0 to 5 is 0 + 1 + 2 + 3 + 4 + 5 = 15.

4. Finding the total number of five-digit numbers:
- To find the total number of five-digit numbers that can be formed using these digits, we need to select one digit for each position (thousands, hundreds, tens, units).
- For the thousands place, we have six options (0, 1, 2, 3, 4, or 5).
- For the hundreds, tens, and units place, we can choose any of the remaining five digits.
- Therefore, the total number of five-digit numbers is 6 * 5 * 4 * 3 = 360.

5. Filtering the numbers divisible by 3:
- Out of the 360 five-digit numbers, we need to find the ones that are divisible by 3.
- To do this, we need to find the numbers whose sum of digits is divisible by 3.
- The sum of digits from 0 to 5 is 15, which is divisible by 3.
- So, we need to find the numbers that have a sum of digits that is either 3, 6, 9, 12, or 15.

6. Counting the numbers divisible by 3:
- To count the numbers that are divisible by 3, we need to find the number of ways we can select digits from the given set (0, 1, 2, 3, 4, 5) to form a number with a sum of digits divisible by 3.
- Let's consider the sum of digits to be 3. In this case, we need to select three digits from the given set.
- The number of ways to select three digits from six is 6C3 = 6! / (3! * (6-3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20.
- Similarly, for sums of digits 6, 9, 12, and 15, we will have 20 ways each.
- Adding up the counts for each sum of digits, we get a total of 20 + 20 + 20 + 20 + 20 = 100.

7. Conclusion:
- Out of the 360 five-digit numbers that can be formed without repetition, 100 of them are divisible by 3.
- Therefore, the correct answer is option D) 216.
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Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are [2002]a)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer?
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Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are [2002]a)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are [2002]a)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are [2002]a)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer?.
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