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How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
- a)5
- b)10
- c)15
- d)20
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 a...
Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
∴ Required number of numbers = (1 x 5 x 4) = 20.
Most Upvoted Answer
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 a...
Analysis:
To form a 3-digit number that is divisible by 5 using the digits 2, 3, 5, 6, 7, and 9 without repetition, we need to consider the following:
Key Points:
- The last digit has to be 5, as the number needs to be divisible by 5.
- The first digit cannot be 0, so it can be any of the remaining 5 digits.
- The middle digit can be any of the remaining 4 digits.
Calculation:
- Number of ways to choose the first digit = 5
- Number of ways to choose the middle digit = 4
- Number of ways to choose the last digit (which is fixed as 5) = 1
- Total number of 3-digit numbers = 5 x 4 x 1 = 20
Therefore, the correct answer is option D) 20.
To form a 3-digit number that is divisible by 5 using the digits 2, 3, 5, 6, 7, and 9 without repetition, we need to consider the following:
Key Points:
- The last digit has to be 5, as the number needs to be divisible by 5.
- The first digit cannot be 0, so it can be any of the remaining 5 digits.
- The middle digit can be any of the remaining 4 digits.
Calculation:
- Number of ways to choose the first digit = 5
- Number of ways to choose the middle digit = 4
- Number of ways to choose the last digit (which is fixed as 5) = 1
- Total number of 3-digit numbers = 5 x 4 x 1 = 20
Therefore, the correct answer is option D) 20.
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How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?a)5b)10c)15d)20Correct answer is option 'D'. Can you explain this answer?
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