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I was watching one of the Khan academy videos on probability. Everything seems fine except where we find that flips are head. We are just picking $3$ outcomes out $2^8$ possible outcomes. How can we sure that head appears more than $2$ times in $8$ flips$?$ What I am missing$?$

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  • $\begingroup$ We are picking ${8\choose 3} = 56$ outcomes out of $2^8$. Note that all the following outcomes fit the description: $HHHTTTTT, HHTHTTTT, HHTTHTTT,\cdots, HHTTTTTH, HTHHTTTT,\cdots,HTTTTTHH, THHHTTTT, \cdots , TTTTTHHH$. $\endgroup$ – Darth Geek Oct 5 '15 at 18:03
  • $\begingroup$ @DarthGeek, there is some parsing error in your comment. $\endgroup$ – CodeYogi Oct 5 '15 at 18:07
  • $\begingroup$ Also, how are we sure that we will get $3$ heads in some of the outcomes? Can't there be the case when there are no $3$ heads? $\endgroup$ – CodeYogi Oct 5 '15 at 18:14
  • $\begingroup$ We are computing the amount of ways we can select three undistinguishable coin flips (heads) out of the total eight. The rest of wich are also undistinguishable (tails). We are ensuring that the outcomes we are selecting have indeed three heads and five tails. Also, I couldn't find the error, do you mind pointing it out to me? $\endgroup$ – Darth Geek Oct 5 '15 at 19:29
  • $\begingroup$ @DarthGeek I see [Math Processing Error] error in your first comment! $\endgroup$ – CodeYogi Oct 5 '15 at 19:31

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