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!

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    $\begingroup$ Welcome to Math SE. What else have you tried so far and are having difficulty with? $\endgroup$ – John Omielan Dec 23 '18 at 1:02
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    $\begingroup$ 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. $\endgroup$ – N. F. Taussig Dec 23 '18 at 1:03

Let me draw you 6 bins:


now let me give you an example:


and another example:


and another example


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)


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