A combinatorics puzzle related to Stars and bars problem The problem goes like: 
A store sells 11 different flavors of ice cream. In how many ways can a customer choose 6 ice cream cones, not necessarily of different flavors?
I tried thinking for 2 days then I gave up and seen solution. The answer was somewhat connected to Stars and bars problem. The question is how can this problem be connected to Stars and bars puzzle? I am not able to see any connection of this puzzle to the problem. For eg: Stars and bars puzzle requires identical object to be distributed in boxes which is not case here.

Yes, Stars and bars technique is the right tool here. Note that you have to count the non-negative integer solutions of
$$x_1+x_2+\dots+x_{11}=6$$
where $x_i$ is the number of icecreams taken from the "box" containing "identical" icecreams all of the $i$-th flavour. 
Can you take it from here? What is the final answer?
