The only numbers that can be made with ONLY 5 and 6 are 56 and 65. That is because 5 and 6 are only 2 numbers. If you wanted a three digit number, you would have to use double of one number. You could say these numbers: 556 566 565 656 665 Other than that, I do not know.
5! = 5 x 4 x 3 x 2 x 1 = 120
The question can be re-stated as asking for the total number of permutations that can be derived from the following two groups of digits: AAABCD and AABBCD, where A, B, C and D are different. The number of ways of choosing the digit A, to be used three times, out of the ten digits {0, 1, 2, ... 9} is 10. Having done that, the number of ways of selecting 3 from the remaining 9 digits is 9C3 = (9*8*7)/(3*2*1) = 84. Thus there are 10*84 = 840 combinations of the form AAABCD. You now need all the distinct permutations of these 6 digits. The total number of permutations of 6 digits is 6! but because 3 of the digits are the same, these permutations are not all distinct. In fact, there are 6!/3! = 120 distinct permutations. That makes a total of 840*120 = 100800 such numbers. Next, the number of ways of choosing the digits A and B, each to be used twice, out of the ten digits {0, 1, 2, ... 9} is 10C2 = (10*9)/(2*1) = 45. Having done that, the number of ways of selecting C and D from the remaining 8 digits is 8C2 = (8*7)/(2*1) = 28. Thus there are 45*28 = 1260 combinations of the form AAABCD. You now need all the distinct permutations of these 6 digits. The total number of permutations of 6 digits is 6! but because 2 pairs of these digits are the same, these permutations are not all distinct. In fact, there are 6!/(2!*2!) = 180 distinct permutations. That makes a total of 1260*180 = 226800 such numbers. The grand total is, therefore, 100800 + 226800 = 327600 6-digit numbers made from 4 distinct digits.
4 and 7
Assuming several things: Numbers can't start with zero; Repeated digits are allowed, then: First digit can be any of 9, Second digit can be any of 10, Third and fourth digits can each be any of 10; There are therefore 9 x 10 x 10 x 10 ie 9,000 possible answers, which by coincidence is the total of the numbers from 1000 to 9999. If howerver you did not intend to allow repeated digits then the first digit can be one of 9, the second also one of 9 (zero now allowable), the third can be one of 8 and the fourth one of 7, giving a total of 9 x 9 x 8 x 7 ie 4536 arrangements, some of which will contain the same four digits but in a different order eg 1234 and 1243. If you don't want this then divide by 24 and get a more manageable 189.
depends on your answer
about 13
2
32C3 = 4960
There are none.Any number made by using the digits 0 to 9 once is divisible by 9 and so not a prime.There are none.Any number made by using the digits 0 to 9 once is divisible by 9 and so not a prime.There are none.Any number made by using the digits 0 to 9 once is divisible by 9 and so not a prime.There are none.Any number made by using the digits 0 to 9 once is divisible by 9 and so not a prime.
There are 24 number made by permutations of the digits. There are lots more if the digits can be repeated, for example, 27335722. Even more can be made by using arithmetic and algebraic operations, for example 35^27 = approx 4.8960*10^41. You have not specified what the rules for "making" numbers are!
24
If you're limited to only 5 digits that can't be repeated, then there are 120 ways they can be arranged.
9,752 9,725 9,572
Six: 234, 243, 324, 342, 423, and 432.
9*9*9 = 729 using the digits 1 to 9 and 2*9 using 10 and another digit. 749 in all.
874321 is the largest number made from all these digits.