Question 885014: Using the digit set (0,1,2,3,4,5) how many 4-digit numbers can be formed if the number must have two zeros and no other repeated digits?
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
We can choose which two of the digits (2nd, 3rd, or 4th) to put zeros
in C(3,2) = 3 ways
The reason this uses combinations and not permutations is because, say, picking
2nd and 4th places to put the two 0's is the same as picking 4th and 2nd, so
ORDER DOES NOT MATTER.
We can chose the remaining two digits in P(5,2) = 20 ways
The reason this is permutations and not combinations is because, say, putting 3
in the left most unfilled digit and 5 in the rightmost unfilled digit is NOT the
same as the vice-versa. So ORDER MATTERS.
Answer C(3,2)*P(5,2) = 3x20 = 60 ways.
Edwin
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