Find the number of seven-digit numbers such that every number is divisible by 125 no number contains a zero and no digit appears more that once in the number?
This seems to be a pretty tough question. Seven digit numbers
range from 1,000,000 to 9,999,999. There are 9,000,000 of them. The
number of these divisible by 125 will be 9,000,000/125 which is
72,000.
If no number contains a zero, and all the digits are different,
then we know two things:
- Since multiples of 125 will end in 5 or 0, our numbers will
all end in 5.
- The other 6 digits must be chosen the eight digits
1,2,3,4,6,7,8,9.
How many ways can you choose 6 things out of 8? This is 8C6. The
number of arrangements of these 6 things would be 8P6. How are you
doing so far - if you're with me then resubmit your question
starting with "Please continue to find the number ..."
