There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability Q that all three secretary are assigned at least one report?
Options:
A) 8/9
B) 64/81
C) 4/9
D) 16/81
E) 5/9
I got the same answer: Here's my reasoning   First Report you have 3 choices   Second Report you have 2 choices   Third Report you have 1 choice   Fourth report 3 choices again   Then total number of ways is: 3*2*1*3=3^2*2   This is not correct. You have assumed that the 4th report must go to someone who already has a report. There is no such constraint. You can easily give the 1st and 2nd reports to secretary 1, 3rd report to secretary 2 and 4th report to secretary 3. But you have ignored all such cases.   The number of ways of ensuring at least one report goes to each secretary is 44/92 (select 2 reports out of 4 which go to the same person)*34/91 (select the person who must type 2 reports)*2! (since you have 2 reports left which you must distribute to the 2 remaining people such that each person gets one) = 36   Required probability Q = 36/81.4/9
<result>C</result>
There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability Q that all three secretary are assigned at least one report?