SOLUTION: 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?

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

Or going back to decimal,

Hope that helps,
Kev
RELATED QUESTIONS
Four-Digit Number. How many four-digit numbers can be formed using the digits 0, 1, 2, 3, (answered by MathLover1,jilalbenkad)

How many odd numbers that exceed 1000 can be formed from the digits 0, 1, 2, 3 and 4 if... (answered by Edwin McCravy)

Given the digits 0, 1, 3, 5, and 6, how many different four-digit numbers can be made... (answered by Edwin McCravy)

How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if... (answered by MathLover1)

How many 7-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 if... (answered by hitarth)

How many four digit numbers can be formed from 0-9 if: repetitions are allowed the... (answered by AnlytcPhil)

How many four digits number can be formed with the 10 digits 0-9 a) If repetitions are... (answered by ikleyn)

How many 3 digit numbers can be formed from the digits 1,3,5 and 7 if repetitions are... (answered by LinnW)

How many four-digit numbers can be formed using the digits 0,1,2,3,4,5,6,7,8, and 9 if... (answered by ikleyn)