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The total number of three-digit numbers, with one digit repeated exactly two times, is ______. (in integers)
Correct answer is '243'. Can you explain this answer?
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Most Upvoted Answer
The total number of three-digit numbers, with one digit repeated exact...
If 0 is taken twice, then number of ways = 9
If 0 is taken once, then 9C1 × 2 = 18
If 0 is not taken, then 9C1 8C1.3 = 216
Total = 243
If 0 is taken once, then 9C1 × 2 = 18
If 0 is not taken, then 9C1 8C1.3 = 216
Total = 243
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Community Answer
The total number of three-digit numbers, with one digit repeated exact...
Explanation:
Total three-digit numbers:
- There are 900 three-digit numbers (100 to 999).
Numbers with all distinct digits:
- There are 9 choices for the hundreds place (1 to 9), 9 choices for the tens place (excluding the digit in the hundreds place), and 8 choices for the units place (excluding the digits in the hundreds and tens places).
- So, the total number of three-digit numbers with all distinct digits is 9 x 9 x 8 = 648.
Numbers with one digit repeated exactly two times:
- There are 9 choices for the repeated digit and 3 choices for the position of the non-repeated digit.
- So, the total number of three-digit numbers with one digit repeated exactly two times is 9 x 3 = 27.
Total number of three-digit numbers with one digit repeated exactly two times:
- Adding these two cases, we get 648 (distinct digits) + 27 (one digit repeated) = 675.
- However, we need to exclude the numbers with all digits being the same (111, 222, ..., 999).
- There are 9 such numbers.
- Therefore, the total number of three-digit numbers with one digit repeated exactly two times is 675 - 9 = 666.
Final Answer:
- The total number of three-digit numbers, with one digit repeated exactly two times, is 666.
Total three-digit numbers:
- There are 900 three-digit numbers (100 to 999).
Numbers with all distinct digits:
- There are 9 choices for the hundreds place (1 to 9), 9 choices for the tens place (excluding the digit in the hundreds place), and 8 choices for the units place (excluding the digits in the hundreds and tens places).
- So, the total number of three-digit numbers with all distinct digits is 9 x 9 x 8 = 648.
Numbers with one digit repeated exactly two times:
- There are 9 choices for the repeated digit and 3 choices for the position of the non-repeated digit.
- So, the total number of three-digit numbers with one digit repeated exactly two times is 9 x 3 = 27.
Total number of three-digit numbers with one digit repeated exactly two times:
- Adding these two cases, we get 648 (distinct digits) + 27 (one digit repeated) = 675.
- However, we need to exclude the numbers with all digits being the same (111, 222, ..., 999).
- There are 9 such numbers.
- Therefore, the total number of three-digit numbers with one digit repeated exactly two times is 675 - 9 = 666.
Final Answer:
- The total number of three-digit numbers, with one digit repeated exactly two times, is 666.
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The total number of three-digit numbers, with one digit repeated exactly two times, is ______. (in integers)Correct answer is '243'. Can you explain this answer?
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The total number of three-digit numbers, with one digit repeated exactly two times, is ______. (in integers)Correct answer is '243'. 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 The total number of three-digit numbers, with one digit repeated exactly two times, is ______. (in integers)Correct answer is '243'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The total number of three-digit numbers, with one digit repeated exactly two times, is ______. (in integers)Correct answer is '243'. Can you explain this answer?.
The total number of three-digit numbers, with one digit repeated exactly two times, is ______. (in integers)Correct answer is '243'. 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 The total number of three-digit numbers, with one digit repeated exactly two times, is ______. (in integers)Correct answer is '243'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The total number of three-digit numbers, with one digit repeated exactly two times, is ______. (in integers)Correct answer is '243'. Can you explain this answer?.
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