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OG Pg. 117 (Orange Book)

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by clubtwofour » Tue Oct 28, 2008 4:31 pm
OG states the following regarding counting methods, "...each time a coin is flipped, there are two possible outcomes, heads and tails. If an experiment consists of 8 consecutive coin flips, then the experiment has 28 possible outcomes, where each of these outcomes is a list of heads and tails in some order."

How did OG calculate that there are 28 possible outcomes? Can someone show the math behind this?
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by lachlanc » Wed Oct 29, 2008 9:52 am
It is a permutation calculation - n!/k!(n-k)!

8C2 = 8!/2!6!

= 8*7/2 = 56/2 = 28
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by clubtwofour » Mon Nov 03, 2008 2:02 pm
That makes sense! Thanks!
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by cramya » Mon Nov 03, 2008 2:42 pm
If I am not mistaken the multiplication principle states that in counting the possibilits of independent events happenning u mutiply the possibilities of these indepenedent events (i.e what comes up in the 2nd flip is independent of what happenned in the 1st flip)


2*2*2*2*2*2*2*2 = 2 ^ 8

Hope this helps!
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by stop@800 » Mon Nov 03, 2008 7:22 pm
I agree with cramya, it should be 2^8.
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by curious_swan » Thu Sep 26, 2013 1:02 pm
when you flip the coin 8 times there are 256 (2^8) possible combinations (outcomes) considering the probability into account for eg.

it can be be

1. H, H, H, H, H, H, H, T
2. H, H, H, H, H, H, T, T
3. T, T, T, T, T. T, T, H
---
--
up to 256 combinations.
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