Number of ways to arrange 4 identical objects in 6 bins.

I am trying to count the number of ways to play 4 indistinguishable objects in 6 bins. Each bin can contain either 0 or 1 object. We can think of this as the number of binary strings of length 6 with exactly four 1's. Thanks!

• Welcome to Math SE. What else have you tried so far and are having difficulty with? – John Omielan Dec 23 '18 at 1:02
• Approaching the problem through binary strings is a good idea. The numbers are sufficiently small that you should be able to list all the possibilities, from which you could then derive a formula. – N. F. Taussig Dec 23 '18 at 1:03

Let me draw you 6 bins:

|_|_|_|_|_|_|


now let me give you an example:

|x|x|x|_|x|_|


and another example:

|x|_|x|_|x|x|


and another example

|x|_|_|x|x|x|


in how many ways can you put those x in 6 bins?

Let me sharpen the question: in how many ways can you choose 4 items from 6? and here's another nice thing to notice...in how many ways can you choose 2 from 6? (hint: same answer)