What is a strictly increasing sequence in discrete math?
Consider selecting $3$ objects from the set $A = \{ 1,2,3,4,5,6\}$, how many strictly increasing sequences can be chosen from $A$? Answer is $C_3^6$, but my problem is that I don't know what it means by strictly increasing and how to get the answer $C_3^6$.
Edit:
Thanks for answering, so is it correct to say that the answer is 6C3 because it's the same thing as a combinations problem without repetition and we can say this because 354 for example is the same as 345 since order doesn't matter. Therefore, 6C3 right?
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$\begingroup$A strictly increasing sequence is a set of elements that have been arranged in ascending order.
Some strictly increasing sequences of elements in $A$ are $\{1,3,4,5\}$, $\{2,4,6\}$, and $\{3,5\}$. Some sequences that are not strictly increasing are $\{3,1,4,5\}$, $\{1,2,2,3\}$, and $\{6,4,2\}$.
The key insight is that for a given group of $3$ elements selected from $A$, there is exactly one way to arrange them in ascending order. That is, for every group of $3$ elements selected from $A$, there is one and only one increasing sequence consisting of the same elements.
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