How many ways to pick up 1 or 3 chocolates from $n$ chocolates?

Question

There are $n$ chocolates. We can pick either $1$ or $3$ chocolates at once. In how many ways can we pick all the chocolates?

The variable $n$ can have any value, $30,100,500$ etc.

What is the general formula for this calculation?

Please, explain!

For an idea: If n=1: There can be one possible way. If n=2: There are two possible ways. One on the first pick, and another one on second. If n=3: There can be 4 combinations. Either all chocolates at once or one by one.

Answer 1

The formula for n choose k is

nCk = n!/(k!(n-k)!)

In your problem, let's say n=10

So choosing 1(k) from 10(n) there are 10 combinations (plug it in the formula)

and choosing 3(k) from 10(n) there are 120 combinations

So choosing 10C1 or 10C3 = 10C1 + 10C3 = 120+10 = 130

I think this is what you are looking for. I studied it long back, peer review is needed.