# Choose k elements from n elements where some elements repeat

I have a set A={20,20,35,20,50,60}.I want choose any 4 elements from the set.How many ways can I choose 4 elements.

As far I know if the elements of the set are distinct the number of ways to choose 4 elements will be $6\choose 4$.Since in this problem the element 20 repeat 3 times some combination will be over-calculated.How can I deal with this situation.

Can anyone explain how I solve the above problem with intuition?

• Actually $A=\{20,35,50,60\}$. If you want to maintain the repetition then you should not choose from a set, but from a tuple $\langle20,20,35,20,50,60\rangle$. Commented Sep 20, 2015 at 17:59
• Since A has repeated elements, it is usually referred to as a multiset. Commented Sep 20, 2015 at 18:10
• Does the order play a role ? Commented Sep 20, 2015 at 18:12

If I were to address this particular problem, I'd look at it ad hoc. That is to say, I would observe that at least one of the $20$ elements must be chosen. So:
• How many different combinations have one $20$?
• How many different combinations have two $20$s?
• How many different combinations have three $20$s?
The answers to each of these three questions can be answered using ordinary combinatorial techniques, and then the answers added up to yield a final result of $7$.