How many 5-digit numbers can be formed from the numbers 0, 2, 4, 5, 7 and 9 (without repetition), such that it is divisible by 4?
Question
How many 5-digit numbers can be formed from the numbers 0, 2, 4, 5, 7 and 9 (without repetition), such that it is divisible by 4?
Solution
To form a 5-digit number that is divisible by 4, the last two digits of the number must be divisible by 4. The possible combinations of last two digits that are divisible by 4 are: 20, 24, 40, 52, 72, 92, 04, 60, 80, 28, 48, 68, 84, 64, 44, 20, 24, 40, 52, 72, 92.
Step 1: Select the last two digits. There are 21 ways to do this.
Step 2: Select the first digit. It cannot be 0 (since it's a 5-digit number), so there are 4 remaining choices (2, 5, 7, 9).
Step 3: Select the second digit. There are 3 remaining choices.
Step 4: Select the third digit. There are 2 remaining choices.
So, the total number of 5-digit numbers that can be formed is 21 (from step 1) * 4 (from step 2) * 3 (from step 3) * 2 (from step 4) = 504.
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