Melody

How many 4-digit numbers have no repeating digits?

If no zeros

9C4*4!

nCr(9,4)*4! = 3024

If there is a zero (zero cannot be the first digit)

9C3*3*3!

nCr(9,3)*3*3! = 1512

3014+1512 = 4526

Thanks Ginger :)

Didn't you like this answer Rictor5?  I thought it was very good.

Thanks guest. :)

If you understood what I have stated as my assumption - then there is no 'BUT'

Wolfram alpha has answered a different question as it has made a different assumption.

This is why questions should be stated exactly with no room for reasonable alternate interpretations.

I never suggested that your answer was incorrect although you should have stated the assumption that you were making.

(i.e. that all the dice were uniquely identifiable)

Hi asinus  :)

You are very welcome.

I'll give you 5 stars for your excellent manners :)

No this is not true with my assumption that I have stated.

The dice are identical so 3,1,1,1 is identical to 1,1,1,3 and 1,3,1,1 and 1,1,3,1

This is NOT 4 ways this is only 1 way. 

Please note that I have assumed all of the dice are identical :)

I can't see any straight forward way to do this.

The 4 dice would have to add up to 6,9,12,15,18,21 or 24

The only way for the dice to add to 24 is   6,6,6,6      that is one combination.

Add to 21

6,6,6,3

6,6,5,4

6,5,5,5,              So there are 3 ways to add to 21

Add to 6

1,1,1,3

1,1,2,2             So there are only 2 ways to add to 6

Add to 9

1,1,1,6

1,1,2,5

1,1,3,4

1,2,2,4

1,2,3,3         that is it I think so that is  5 ways

Add to 12

1,1,4,6,

1,1,5,5

1,2,3,6

1,2,4,5

2,2,2,6

2,2,3,5

2,2,4,4

2,3,3,4

3,3,3,3        that seems to be 9 ways

Add to 15

1,2,6,6

1,3,5,6

1,4,5,5

1,4,4,6

2,2,5,6

2,3,4,6

2,3,5,5

2,4,4,5

3,3,3,6

3,3,4,5

3,4,4,4       there seems to be 11 there

add to 18     (I am going to try and do it differently - in pairs this time)

6+12            1,5,6,6

                     2,4,6,6

                     3,3,6,6

7+11             1,6,5,6

                     2,5,5,6

8+10            6,2,6,4 

                     6,2,5,5

                     5,3,4,6

                      5,3,5,5

                      4,4,4,6

                      4,4,5,5                     

9+9               6,3,6,3,

                     6,3,4,5                      That seems to be 11 ways

6                  2 ways

9                  5 ways

12                9 ways

15               11 ways

18              11 ways

21                3 ways

24                1 way

So if I haven't made any mistakes I get   2+5+9+11+11+3+1 =2+5+9+11+11+3+1

= 42 ways of thowing a multiple of 3