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February 17th, 2014, 03:12 AM   #1
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Four-digit number

Hi,
How many four-digit number which each digit smaller than previous digit?
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February 17th, 2014, 03:22 AM   #2
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Re: Four-digit number

Also posted here: viewtopic.php?p=193943#p193943

You can pick 10 digits (you won't get a leading 0). You want them all distinct, since the next digit is smaller then the preceding.

For the first digit, you have 10 choices.
AND for the second digit, you have 9 choices, given that you can't pick the one you already picked
AND for the third digit, you have 8 choices, given that you can't pick the ones you already picked
AND for the fourth digit, you have 7 choices, given that you can't pick the ones you already picked

Due to the AND's, you may multiply the amount of choises. Gives 10 * 9 * 8 * 7.
The four digits are distinct. Four distinct digits can be sorted in 4 * 3 * 2 * 1 = 24 ways. So divide by 24.

Gives 10 * 9 * 8 * 7 / (4 * 3 * 2 * 1) =
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February 17th, 2014, 05:24 AM   #3
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Re: Four-digit number

3210 ... 9876 : 210

1234 ... 6789 : 126
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