Probability question of flipped coins

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The probability of obtaining the specific sequence HTHHTTTHTHHHTHHHHTHT when flipping 20 fair coins is calculated by recognizing that there is only one successful outcome among the 2^20 total possible outcomes. When considering the order of heads and tails, the probability is 1/2^20. If the order does not matter, the number of successful outcomes is given by the combination C(20,12), which represents the ways to choose 12 heads from 20 flips. The probability in this case is the number of combinations divided by the total outcomes, resulting in C(20,12)/2^20. Understanding these calculations is essential for solving similar probability questions involving coin flips.
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Homework Statement



suppose you flip 20 fair coins. what is the probability of getting the sequence HTHHTTTHTHHHTHHHHTHT in exactly that order?

What if the order doesn't matter?

Homework Equations





The Attempt at a Solution


Ok so in general the total possible outcomes are 2^20.
and the #ways you can get 12 H (or the multiplicity) would be 20!/(12!(20-12)!) right?
i don't how how to account for the order, or switch it to probability
 
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You know everything you need to know. There are 2^20 possibilities. If you account for order, there's only one way to succeed. If you don't there are C(20,12) ways, as you said. The probability is the number of ways to succeed over the total number of possible ways.
 

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