Question 847478: Determine the number of separate outcomes
n = 5, x = 2
n = 11, x = 9
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! Imagine you were flipping a coin.
How many outcomes consist of exactly 2 heads out of 5 flips?
HHTTT HTHTT HTTHT HTTTH THHTT THTHT THTTH TTHHT TTHTH TTTHH
There are 10. Another way we can look at this is (5 choose 2) which you will see is 10.
Using this logic, (11 choose 9) will be the number of separate outcomes which is 55.
So, the binomial coefficient at the beginning of the binomial formula is the total number of distinct outcomes... that is (n choose x).
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