How many 9 digit numbers are possible by using the digits 1,2,3,4,5 which are divisible by 4 if the repetition is not allowed?
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Digits that can be used = 1, 2, 3, 4 and 5
For a number to divisible by 4, the last two digits have to be divisible by 4
So, the units digit cannot be 1, 3 or 5
If the units digit is 2, only 12, 32 adn 52 are acceptable as the last two digits
If the units digit is 4, only 24 and 44 are acceptable as the last two digits.
So, total 5 cases for the last two digits.
Now, the first 7 digits of the 9 digit number can be filled in 57 ways as each place can be filled by 1, 2, 3, 4 or 5.
So, desired answer = 57*5 = 58
For a number to divisible by 4, the last two digits have to be divisible by 4
So, the units digit cannot be 1, 3 or 5
If the units digit is 2, only 12, 32 adn 52 are acceptable as the last two digits
If the units digit is 4, only 24 and 44 are acceptable as the last two digits.
So, total 5 cases for the last two digits.
Now, the first 7 digits of the 9 digit number can be filled in 57 ways as each place can be filled by 1, 2, 3, 4 or 5.
So, desired answer = 57*5 = 58
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