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How many three digits numbers contain only 5 and 6?
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.
How many 6 digit numbers can be formed with 4 different digits?
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.
How many 5 digit numbers can be made using the numbers 4 1 7 8 2?
5! = 5 x 4 x 3 x 2 x 1 = 120
What digits are made up of only line segments in 24357?
4 and 7
How many 4 digit numbers can be made out of the numbers 0-9 and what are they?
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.
