SOLUTION: What is the number of different 7 digit numbers that can be made by rearranging the digits 3053354?

Question 30425: What is the number of different 7 digit numbers that can be made by rearranging the digits 3053354?
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
if all the numbers were different, we would have 7! permutations... which is 5040 different numbers.

Additional thing to think about would be numbers like 0123456.. this is not a recognised number, so we cannot have the zero in the "first position".

So...
First position: how many numbers could we have? Answer is 6 (as the zero is not allowed there).

Second position: how many numbers? Well any of the 6 remaining.
Third position: Any of the 5 remaining
fourth position: Any of the 4 remaining
and so on.

Total: 6*6*5*4*3*2*1 --> 6*6! --> 6*720 --> 4320.

Notice, this is 720 less than 5040 ie it is one whole block of 6!

Now, this is not the final answer, since there are three 3's and two 5's, so there is going to be repetition of certain numbers.

Total number of different numbers = 4320/(3!2!)
Total number of different numbers = 4320/(6*2)
Total number of different numbers = 4320/12
Total number of different numbers = 360

So, there are just 360 different numbers that can be made up from the given set of digits.

jon.

RELATED QUESTIONS
How many different seven digit numbers can be made by rearranging the digits... (answered by stanbon)

You are given the following seven-digit number: 4064465. How many different... (answered by Edwin McCravy)

how many different four digit numbers can be formed by rearranging the digits of... (answered by ikleyn)

What is the greatest even number you can create by rearranging the digits of... (answered by Ed Parker)

If only the digits 0, 1, 3, 4, 5, 6, and 7 may be used, find the number of possible... (answered by greenestamps,Alan3354)

Ed made a list of all the two-digit numbers that can be formed using two different digits (answered by richwmiller)

how many different four digit pin numbers can be made from the digits 2,3,4,5 A=if the... (answered by Edwin McCravy)

How many numbers of 5 digits can be made from the digits 1,2,3,4,5,6,7,8 and 9 when each... (answered by ikleyn)

How many different license plates can be made that have one letter followed by 4... (answered by Edwin McCravy)