Can someone help me on this problem?
How many vectors (x1,x2......xk) are there for which each xi is a positive
integer such that 1<= xi<=n and x1<x2<.......<xk?
thanks in advance!
If , the answer is 1:
If , the answer is 0.
If , we're actually looking at how many k-lengthed increasing sequences there are with entries in
You should note that for any elements that we choose, there may only be one such sequence. Also, you can choose any elements and then simply set them in order. This gives us that there are options.