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ow many five digit numbers can be formed using the digits 0, 2, 3,4and 5, when repetition is allowed such that the number formed is divisible by 2 and 5?
- a)100
- b)150
- c)3125
- d)500
- e)125
Correct answer is option 'D'. Can you explain this answer?
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ow many five digit numbers can be formed using the digits 0, 2, 3,4and...
The correct answer is 500.
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ow many five digit numbers can be formed using the digits 0, 2, 3,4and...
To form a five-digit number that is divisible by both 2 and 5, the number must end with either 0 or 5.
We have 5 digits to choose from: 0, 2, 3, 4, and 5.
If the number ends with 0, there are 4 choices for the first digit (2, 3, 4, or 5) and 4 choices for each of the remaining three digits. So, there are 4 x 4 x 4 = 64 numbers that end with 0.
If the number ends with 5, there are also 4 choices for the first digit (0, 2, 3, or 4). However, in this case, the remaining three digits can be any of the 5 choices (0, 2, 3, 4, or 5) since repetition is allowed. So, there are 4 x 5 x 5 x 5 = 500 numbers that end with 5.
Therefore, the total number of five-digit numbers that can be formed is 64 + 500 = 564.
However, we need to subtract 1 from this total because 00000 is not considered a five-digit number.
Therefore, the final answer is 564 - 1 = 563.
Since none of the given options match this answer, it appears that none of the options provided are correct.
We have 5 digits to choose from: 0, 2, 3, 4, and 5.
If the number ends with 0, there are 4 choices for the first digit (2, 3, 4, or 5) and 4 choices for each of the remaining three digits. So, there are 4 x 4 x 4 = 64 numbers that end with 0.
If the number ends with 5, there are also 4 choices for the first digit (0, 2, 3, or 4). However, in this case, the remaining three digits can be any of the 5 choices (0, 2, 3, 4, or 5) since repetition is allowed. So, there are 4 x 5 x 5 x 5 = 500 numbers that end with 5.
Therefore, the total number of five-digit numbers that can be formed is 64 + 500 = 564.
However, we need to subtract 1 from this total because 00000 is not considered a five-digit number.
Therefore, the final answer is 564 - 1 = 563.
Since none of the given options match this answer, it appears that none of the options provided are correct.
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ow many five digit numbers can be formed using the digits 0, 2, 3,4and 5, when repetition is allowed such that the number formed is divisible by 2 and 5?a)100b)150c)3125d)500e)125Correct answer is option 'D'. Can you explain this answer?
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