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Permutations: Level 3 Challenges


How many positive integers have no repeated digits?

The number of seven digit integers, with the sum of digits equal to 10 and formed by using the digits 1,2 and 3 only is,

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How many 8 digit numbers are there, such that they are divisible by 9 and all of the digits are distinct?

How many ways can you arrange 5 identical Rooks on a 6 by 10 Chessboard in such a way that none of the rooks attack each other ?

Consider all the 7-digit numbers containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once and that are not divisible by 5. They are arranged in a list in increasing order. Find the 2000th number in this list.


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