Answer:
16.39%
Step-by-step explanation:
We have a total number of forms, which are as follows:
-Harry Potter will serve as President AND Ron will serve as Vice President AND anyone will serve as Treasurer:
p1 = 1P11 = 11! / (11-1)! = 11
-Harry Potter will serve as President AND Hermione will serve as Vice President AND anyone who serves as Treasurer is:
p2 = 1P11 = 11! / (11-1)! = 11
- Harry Potter will not serve as President means that no one except Harry Potter (12 remaining students) serve in three locations:
p3 = 12P3 = 12! / (12-3)! = 1320
in total it would be:
11 + 11 + 1320 = 1342
Now the favorable cases are:
- Hermione becomes the president of this group, which means that anyone except Hermione and Harry Potter (11 remaining students) serve in the remaining two places:
p1 = 11P2 = 11! / (11-2)! = 110
- Ron becoming the president of this group means that anyone except Ron and Harry Potter (remaining 8 students) serve in the remaining two places:
p2 = 11P2 = 11! / (11-2)! = 110
adding it would be: 110 + 110 = 220
now then the final probability is the favorable cases among the totals:
220/1342 = 0.1639
Which means that the probability is 16.39%
