Question 1147432
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(a)  There are 7 item in the Joanna's list.

     7 distinguishable items can be arranged by 7! = 7*6*5*4*3*2*1 = 5040 ways.



(b)  If "scores" are fixed as the first item in the list, it reduces the number of possible arrangements 

     of all other items from 7! to 6! = 6*5*4*3*2*1 = 720.


     Therefore, the fraction of rankings with "scores" at the first position to the total number of arrangements is


          {{{6!/7!}}} = {{{1/7}}}.
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Answered, completed, solved and explained in all details.