If I have 10 numbers [ 0-9 ], how many 4 digit combinations can I make where the 4 digits are not the same?

Question

and how many combi with 3 similar digitsand how many with 2 similar digits?

there are in total 5 grps of combis of 4 digit numbers.... 2 same, 3 same,4 same and 4 different numbers. they should add up to 10000.

THEY SHOULD ADD UP TO 10,000.

Answer 1

0 similar = 10*9*8*7 = 5040
3 similar = 10*9 = 10*C(4,3)*9 = 360
2 similar = C(10,1)*C(4,2)*9*8 = 4320
4 similar = 10

Answer 2

OK, if I understood correctly your problem, let's do this by reasoning:
1) For TWO digits numbers - first you select the most significant digit: you have 9 possibilities to choose from (because it does not make sense to have "zero" as a MSD -- 01 is not a valid two-digit number); then, you select the second digit: this time you admit using "zero" but not the digit already selected as MSD, therefore you have another 9 possibilities, for each particular choice made at step one (it's a "everyone with eachother" combination scheme, let's say...). So, the total number of combinations of differently chosen digits to make up a two-digit number is --> 9 * 9 = 81.
Following the same principle:
2) The third digit you choose cannot be one of the previously two already set, meaning you have only 8 possibilities remaining. You have then --> 9 * 9 * 8 = 648.
3) For four digits --> 9 * 9 * 8 * 7 = 4536.

Of course, the answer can be formalized by using arrangements, permutations and combinations, but I think it's much clearer like this... If you want to know how many combinations can be made, if you don't allow the reordering of digits from a chosen set (accept 1234, but not 2143, or 4132, or 3124, ...), just post another question !... ;) Take care !

Whoops !... Just read the Additional Info... For numbers with 4 digits, none repeating, you already got your answer (4536). If we make 2 digits to be similar, we have --> 9 * 9 * 8 = 648 (you may have noticed it's the same result as for the 3-digit none repeating number problem -- that's because IT IS practically the same problem, only you write a digit twice to obtain a 4 digit number). For 3 repeating digits (obviously now) --> 9 * 9 = 81. And for all 4 digits to be similar, I guess there no need to compute the answer: it's --> 9 (from 1111 to 9999)
If you sum these up, you get: 4536 + 648 + 81 + 9 = 5274. Can you answer why the difference to 10,000? ;)

Answer 3

Since your question didn't say anything about uniqueness - in other words, if the combination of 1234 is the same as 4321 - then the answer is 10 * 9 * 8 * 7 = 5040, or 10! (factorial) divided by 6!.

Similarly, for 3 digits it's 10 * 9 * 8 or 720, or 10!/7!, and for two it is 10 * 9 or 90, or 10!/8!.

If uniqueness makes a difference - if 1234 and 4321 are considered the same combination - then it gets more complicated. But if that was a factor you would have included that, right?

Answer 4

the digit upfront cannot be 0.so the choice for the first digit is9.the next digit can be 0 so leaving the no chosen as the first digit the choice will be 9 again.for the third digit the choice will be 8 and for the last digit the choice will be 7
so the permutation will be 9*9*8*7=4536
with three similar digits
the first three digits being the same will be 9*1*1*9=81
the first,third and the fourth being the same will be=9*1*1*9=81
the first,second and fourth being the same=9*1*1*9=81
the second third and the fourth being the same=9*9*1*1=81
with the first and the second digit being the same=9*1*9*9=729
the first and the third digit being the same=9*9*1*9=729
the first and the fourth digit being the same=9*9*9*1=729
the second and the third digit being the same=9*9*1*8=648
the second and the fourth digit being the same=9*9*8*1=648
the third and the fourth digit being the same=9*9*8*1=648
so the combinations wher the four digits are not the same=4536
with three similar digits=324
with two similar digits=4131

Answer 5

4 digit combinations: 10 * 9 * 8 * 7 = 5,040
3 digit combinations: 10 * 9 * 8 = 720
2 digit combinations: 10 * 9 = 90

Answer 6

4 digits not same

10*9*8*7 = 5040

3 similar digits

10*10*10*9 = 9000

2 similar digits

10*10*9*8 = 7200

Answer 7

10*9*8*7

Answer 8

0 is the answer

Answer 9

10x9x8x7=5040 different combinations.