Question 75890: How many four-digit numbers can be formed from the digits 0,1,2,3,4,5 if no repetitions are allowed and 0 cannot be the first digit?
Answer by kev82(151)   (Show Source):
You can put this solution on YOUR website! Your question is a bit ambiguous, can I use each of those digits once, or as many times as I like?
If I can only use each digit once, then there are 5 choices for the first digit(1,2,3,4,5), 5, for the second(0,the four that are left), 4 for the third(we've used two), and 3 for the fourth, making 5*5*4*3=300.
If I can use each digit as many times as I like then there are 5 choices for the first digit and 6 choices for the second, third, and fourth digit, making 5*6*6*6=1080. Interestingly, you can work this out another way. If you think about it, an integer, x, is the number of non-negaitive integers strictly less than it, eg below five there are five non-negative integers 0,1,2,3,4. We are only interested in 4 digit numbers, and are working in base 6 so the answer is clearly _{10}) Or going back to decimal, =5.6^3)
Hope that helps,
Kev
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