How many ways are there to pick r objects from n objects when each object appears an odd number of times

Question

I had misunderstood this problem earlier, and wanted to try again in the correct way, and I think I've got the correct start but I'm not sure how to progress.

So from reading my notes here's what I came up with if i want to pick r objects from n objects but only when each object appears an odd number of times, then for each object I would have the following

object is picked once x

object is picked thrice $x^{3}$

object is picked five times $x^{5}$

and so on... so I think you would get

$(x+x^{3}+x^{5}... +x^r)$

now if this is how many ways I can pick it for one object for n I think I can do

$(x+x^{3}+x^{5}... +x^r)^{n}$

Now I'm not sure where to go from here, or if I've done it correctly up until this point.

Yes this is a duplicate post but the original was completely wrong, thank you for you help.

Answer 1

Using combination:- C(n,1)+C(n,3)+C(n,5)+..... = 2^(n-1)