Question 309212: How many different 6-digit license plates can be made if the first digit must not be 0 and no digits may be repeated?
So far I have tried the 'Fundamental Counting Principle', but I cannot seem to get the answer. I have tried 9!, but that answer makes no sense, I just do not know what to do! Please Help! Thank you.
Found 2 solutions by solver91311, scott8148:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
There are a total of 10 digits counting zero. So if you must exclude zero for the first digit, then there are 9 possibilities for the first digit.
For each of those 9, and since I can now use zero but cannot repeat the first digit, there are 9 choices (the 9 I had to begin with plus one for the zero becoming available, and minus one for the one I used on the first digit). 9 times 9 = 81
For each of those 81 combinations, I now have 8 choices -- the nine I had when I chose the second digit, minus the one that I chose. 81 times 8
For the 4th digit, I have 7 choices. 81 times 8 times 7
And then for the 5th and 6th digits I have 6 and 5 choices:
81 times 8 times 7 times 6 times 5 = (you do your own arithmetic)
John
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! you have 9 choices for the first digit
9 numbers remain for the other 5 digits ___ 9 things, 5 at a time, order counts ___ 9P5
different 6-digit plates ___ 9 * 9P5
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