I have the numbers 1 through 7, and need to know the number of combinations where I choose 4 of them, such that they are strictly increasing from left to right.
Number of Combinations of set {1,2,...7} strictly increasing
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combinatorics
1 Answers
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The key here is to realize that for any 4 numbers you choose, there is only one way to put them in increasing order. So the answer is simply 7 choose 4, or 35 ways.
If you want to use permutations, think of it this way: there are 7*6*5*4 = 840 ways to choose a 4 number sequence. For any given set of 4 numbers, there are 4! = 24 orders you can put them in. Of those, 23 are not in increasing order and 1 is. So 1 out of 24 permutations works, and there are 840 permutations, so there are 840/24 = 35 possible options.
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0k thanks, haha made that harder than it need to be in my head... – 2017-01-14
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0@Rance you probably mean "increasing" not "decreasing" there, though both are true. – 2017-01-14
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0@Stella Biderman thanks, corrected. – 2017-01-14