Probability of A Between B & C in 8-Person Line

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SUMMARY

The probability of person A being positioned between persons B and C in a line of 8 people can be calculated using combinatorial methods. Specifically, there are 6 possible arrangements of A, B, and C that satisfy the condition of A being between B and C. The total number of arrangements of the 8 people is 8!, leading to a probability of A being between B and C as 6/56 or approximately 0.107. This conclusion is derived from analyzing the permutations of the individuals in the line.

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tommyleehutch
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There are 8 people in a line to see a movie.
A,B,C are in the line.
What is the probability that A is in between B and C?

(I can explain more, but don't want to throw in too much to confuse).
BTW there is 8 people in the line.
 
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Hi tommyleehutch ! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
Could you answer if only A, B, and C were in line?

Here's another hint. Is there anything "special" about A?

I notice it has been 3 hours since you asked this. In that time you could have listed all possible lines and counted how many have A between B and C!
 

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