SOLUTION: And one last question: A coin is tossed 12 times. Find the probability getting exactly 6 heads. I know 4096 possibilities... and that is about it :(

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Question 1075293: And one last question:
A coin is tossed 12 times. Find the probability getting exactly 6 heads.

I know 4096 possibilities... and that is about it :(

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
Khan Academy has a great tutorial where they answer the question:
What is the probability of getting exactly 3 heads when you have
5 tosses of a coin. This is the location of the video:
https://www.khanacademy.org/math/precalculus/prob-comb/prob-combinatorics-precalc/v/exactly-three-heads-in-five-flips
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They conclude that the the probability is:
[ number of combinations of ways to get 3 heads in 5 tosses ] / [ 2^5 total possible outcomes ]
or, C( 5,3 ) / 2^5
and
C( 5,3 ) = +%28+5%2A4%2A3+%29%2F%28+3%2A2%2A1+%29+=+60%2F6+
C( 5,3 ) = +10+
and
+10%2F32+=+5%2F16+
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If you repurpose this for your problem, you have:
C( 12,6 ) / 2^12
C( 12,6 ) = +%28+12%2A11%2A10%2A9%2A8%2A7+%29+%2F+%28+6%2A5%2A4%2A3%2A2%2A1+%29+
C( 12,6 ) = +665280+%2F+720+
C( 12,6 ) = +924+
and
C( 12,6 ) / 2^12 = +924+%2F+4096+
C( 12,6 ) / 2^12 = +231+%2F+1024+
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The clip from Khan Academy does a perfect job of
explaning this. Hope it helps.