If you have 5 bannanas and 5 apples and two carrots, and the two carrots are lined up with the 10 fruits at random, what is the probability there are exactly two apples and any number of carrots between the two carrots. Assume that all items are distinct objects.
Attempt: So there are 10! ways to order the 5 bannanas and 5 apples. For each ordering, you can place the carrots in (11 choose 2) slots. So the denominator is 10!*(11 choose 2).
Now we have to find all the points in the sample space where there exactly two apples, and any number of carrots between the two carrots. This is where I am stuck.