How many four-digit numbers can be formed from the digits {0,1,2,3,4,5,6,7,8,9}, given the following conditions:
• repititions are allowed and the number must be seven
• repititions are allowed and the number must be divisible by 5
• the number must be odd and less than 4,000 with repitition allowed.
• repititions are allowed and the number must be seven
• repititions are allowed and the number must be divisible by 5
• the number must be odd and less than 4,000 with repitition allowed.
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Answer:
My attempt to solve this problem is:
First digit cannot be zero, so the number of choices only 6(1,2,3,4,5,6)
The last digit can be pick from 0,2,4,6, so the number of choices only 4
Second digit can be only pick from the rest, so the number of choices only 5
Third digit can be only pick from the rest, so the number of choices only 4
The total number of choices is 6⋅4⋅5⋅4=480
So, is my solution true? Or I miss something? Thanks
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