how many numbers between 2000 and 4000 can be formed with the digits 1,2,3,4,5,6 if repetition is not allowed
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Four things can be ordered in 4! = 24 ways, but 1 or 4 cannot be in the first position only 2 or 3. As half of these numbers start with 1 or 4 , those remaining are 1/2 of 24 or 12.
There are only 2 numbers allowed for the first number, any of the three remaining for the second and any of the two remaining for the third. Don’t care about the last its the only one left. = 2 * 3 * 2 = 12
Almost the same as 2. above. Two numbers for the first position followed by the 3! permutations of what’s left 2*3! = 12
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