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Re: How many integers between 4000 and 7000 have digits that are all diffe [#permalink]
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Digits that can take the thousandth's place = {4, 5, 6}
Digits that can take the remaining places = {5, 6, 7, 8, 9}

If the first digit is 4, then the remaining three digits can be found by 5C3 which is 10.
If the first digit is 5 then the remaining three digits can be found by 4C3 which is 4.
If the first digit is 6 then remaining three digits can be found by 3C3 which is 1.

Adding up: 10+4+1 = 15.
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How many integers between 4000 and 7000 have digits that are all diffe [#permalink]
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six numbers are possible: 4, 5, 6, 7, 8 and 9
0 is not possible, as the order of digits must be increasing
combination of six numbers will contain the unique arrangements of four numbers, increasing in the order (this is a gist)
hence, \(6C4=15\) is the answer
Carcass wrote:
How many integers between 4000 and 7000 have digits that are all different and that increase from left to right?

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