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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)20
- b)16
- c)8
- d)24
Correct answer is option 'A'. 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 * 5 * 4) = 20.Most Upvoted 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.
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.
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How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 a...
Solution:
To form a 3 digit number that is divisible by 5, the units digit must be either 5 or 0.
If the units digit is 5, then we have 5 choices for the units digit (2, 3, 6, 7, or 9) and 4 choices for the hundreds digit (the remaining digits that are not used for the units digit).
Therefore, there are 5 × 4 = 20 three-digit numbers that can be formed with a units digit of 5.
If the units digit is 0, then we only have 1 choice for the units digit (0) and 4 choices for the hundreds digit (the remaining digits that are not used for the units digit).
Therefore, there are 1 × 4 = 4 three-digit numbers that can be formed with a units digit of 0.
Thus, the total number of three-digit numbers that can be formed from the given digits which are divisible by 5 and none of the digits is repeated is 20 + 4 = 24.
However, we need to eliminate the numbers that have a repeated digit. There are 4 such numbers: 225, 255, 665, and 775.
Therefore, the final answer is 24 - 4 = 20.
Hence, option 'A' is the correct answer.
To form a 3 digit number that is divisible by 5, the units digit must be either 5 or 0.
If the units digit is 5, then we have 5 choices for the units digit (2, 3, 6, 7, or 9) and 4 choices for the hundreds digit (the remaining digits that are not used for the units digit).
Therefore, there are 5 × 4 = 20 three-digit numbers that can be formed with a units digit of 5.
If the units digit is 0, then we only have 1 choice for the units digit (0) and 4 choices for the hundreds digit (the remaining digits that are not used for the units digit).
Therefore, there are 1 × 4 = 4 three-digit numbers that can be formed with a units digit of 0.
Thus, the total number of three-digit numbers that can be formed from the given digits which are divisible by 5 and none of the digits is repeated is 20 + 4 = 24.
However, we need to eliminate the numbers that have a repeated digit. There are 4 such numbers: 225, 255, 665, and 775.
Therefore, the final answer is 24 - 4 = 20.
Hence, option 'A' is the correct answer.
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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)20b)16c)8d)24Correct answer is option 'A'. Can you explain this answer?
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