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Numbers greater than 1000 but not greater than 5000 are to be formed with the digits 0, 1, 2, 3, 5, allowing repetitions, the number of possible numbers is
- a)370
- b)375
- c)365
- d)none of these.
Correct answer is option 'B'. Can you explain this answer?
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Numbers greater than 1000 but not greater than 5000 are to be formed w...
**Problem Analysis**
To find the number of possible numbers that can be formed using the digits 0, 1, 2, 3, and 5, we need to determine the number of choices we have for each digit position in the number.
Since we are allowed to repeat digits, we have the following possibilities for each digit position:
- Thousands place: 1, 2, 3, or 5 (4 choices)
- Hundreds place: 0, 1, 2, 3, or 5 (5 choices)
- Tens place: 0, 1, 2, 3, or 5 (5 choices)
- Ones place: 0, 1, 2, 3, or 5 (5 choices)
Therefore, the total number of possible numbers is given by the product of the number of choices for each digit position:
Total number of possible numbers = 4 choices for thousands place * 5 choices for hundreds place * 5 choices for tens place * 5 choices for ones place
**Solution**
To solve the problem, we calculate the product of the number of choices for each digit position:
Total number of possible numbers = 4 * 5 * 5 * 5 = 500
However, we need to find the number of numbers greater than 1000 but not greater than 5000. This means the thousands place cannot be 0.
So, the number of possible numbers is:
Total number of possible numbers = 3 choices for thousands place * 5 choices for hundreds place * 5 choices for tens place * 5 choices for ones place
Total number of possible numbers = 3 * 5 * 5 * 5 = 375
Therefore, the correct answer is option B) 375.
To find the number of possible numbers that can be formed using the digits 0, 1, 2, 3, and 5, we need to determine the number of choices we have for each digit position in the number.
Since we are allowed to repeat digits, we have the following possibilities for each digit position:
- Thousands place: 1, 2, 3, or 5 (4 choices)
- Hundreds place: 0, 1, 2, 3, or 5 (5 choices)
- Tens place: 0, 1, 2, 3, or 5 (5 choices)
- Ones place: 0, 1, 2, 3, or 5 (5 choices)
Therefore, the total number of possible numbers is given by the product of the number of choices for each digit position:
Total number of possible numbers = 4 choices for thousands place * 5 choices for hundreds place * 5 choices for tens place * 5 choices for ones place
**Solution**
To solve the problem, we calculate the product of the number of choices for each digit position:
Total number of possible numbers = 4 * 5 * 5 * 5 = 500
However, we need to find the number of numbers greater than 1000 but not greater than 5000. This means the thousands place cannot be 0.
So, the number of possible numbers is:
Total number of possible numbers = 3 choices for thousands place * 5 choices for hundreds place * 5 choices for tens place * 5 choices for ones place
Total number of possible numbers = 3 * 5 * 5 * 5 = 375
Therefore, the correct answer is option B) 375.
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Numbers greater than 1000 but not greater than 5000 are to be formed with the digits 0, 1, 2, 3, 5, allowing repetitions, the number of possible numbers isa)370b)375c)365d)none of these.Correct answer is option 'B'. Can you explain this answer?
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