Question 1147432: Joanna is running for senior class president. She asks her peers to complete a survey ranking the following in order of importance to them: sports, clubs, test scores, prom, school lunch quality, administrative consequences, and study halls.
a). How many different rankings are possible?
b). What fraction of the possible rankings put test scores first?
Answer by ikleyn(52851)   (Show Source):
You can put this solution on YOUR website! .
(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
 =  .
Answered, completed, solved and explained in all details.
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