Permutation

[E.mendiola]

It's been ages since taking statistics in college and decided to some problems from a textbook with answers to compare. Of the problems which I attempted, this exercise began with a correct total of events but I am not satisfied with a discrepancy between my result and answer problem albeit the difference is 0.000000114 and cannot attribute it to any rounding-off. I am NOT seeking an answer, but an understanding where I may have made an incorrect assumption for part (b) and perhaps a hint or consideration. Please refer to attachment. The yellow highlight is the result from my attempt while the green highlight represents the author's conclusion.

 

[Cubist]

I agree with your answer.

A simpler method to obtain N_xxx is to spot that you're just permuting {a,b,c,d} and for each result the letters are duplicated 3 times to give the required chain. For example one permutation is {a,b,d,c} and this represents the chain aaabbbdddccc. Therefore N_xxx is simply 4! = 24

It looks likely that the author calculated 24/369000. Obviously the bold '0' ought to be a '6'!

 

[Steven G]

I agree with Cubust that your answer is correct.

 

[E.mendiola]

Cubist, thanks for pointing out the possible fat finger input by the author. BTW, I wanted to use the technique where I divided out duplicates to test my interpretation of permutations. A few days later, I realized that the condition placed on placement resembled a simplified version as you mentioned...but it too yielded 24 which just threw me back into a loop trying to figure out how the difference in our answers occurred. Because of your validation of my approach and your explanation of a possible reason for the difference in result, I can now sleep easy knowing there isn't an elusive interpretation somewhere out there yielding a different but correct result....