SOLUTION: An unbiased coin is tossed 13 times. In how many ways can the coin land tails either exactly 9 times or exactly 2 times?

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Question 1111681: An unbiased coin is tossed 13 times. In how many ways can the coin land tails either exactly 9 times or exactly 2 times?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
The 13 tosses can be thought of as 13 places to hold results. In one case we want to distribute two identical items in those 13 places (13C2) and in the other, 9 identical items are distributed amongst the 13 spaces (13C9).
Then we add them because they are two distinct scenarios:

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Dear student,
+nCr+=+n%21%2F%28%28n-r%29%21r%21%29+
+13C2+=+13%21%2F%28%2811%21%29%282%21%29%29+=++13%2A12%2F2+=+78+ <<< the 11! cancels all but 13*12 in the numerator
+13C9+=+13%21%2F%28%284%21%29%289%21%29%29+=+715+ <<< here, 9! cancels most of the numerator
Hope this clears it up!