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 February 17th, 2014, 02:12 AM #1 Senior Member   Joined: Feb 2014 Posts: 114 Thanks: 1 Four-digit number Hi, How many four-digit number which each digit smaller than previous digit?
 February 17th, 2014, 02:22 AM #2 Math Team   Joined: Apr 2010 Posts: 2,778 Thanks: 361 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) = ${10 \choose 4}$
 February 17th, 2014, 04:24 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,906 Thanks: 883 Re: Four-digit number 3210 ... 9876 : 210 1234 ... 6789 : 126

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