Here's a simple problem for you.
You are given $$$n=200$$$ elements and you have to iterate over all possible quadriplets (4) of them, the order of elements of each quadriplet doesn't matter, and you can take same element more than one time. Give quick approximation of how many iterations will algorithm run.
Answer
It is not $$$1,6*10^9$$$
So if you have to iterate over all subsets of length $$$k$$$, it is important to remember to divide running time by $$$k!$$$. In fact, if $$$k=6$$$, you can fit in one second with $$$n<=85$$$, while $$$85^6≈3*10^{11}$$$, but you would iterate only $$$≈5*10^8$$$ subsets, and not knowing that you might not even think of it.
I hope this blog will help, because I was doing same mistake for a long time.
