Probability

newton9 wrote:There are three secretaries who work for four departments. If each of the four departments has one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability that all three secretaries are assigned at least one report?

[spoiler]Answer is 8/9[/spoiler]

total number of cases= 3^4 (each file can be assigned to any of the three secs).

Now, first distribute 1 file each to one sec.

File1 can be assigned to any of the three, then File2 to any of the remaining 2, and file File3 to the remaining sec.

hence, total ways in which this can be done = 3*2*1

One this is done, the fourth file can be given to any of the 3 secs. therefore, number of ways to distribute 4 files

= 3*2*1 * 3

You can start with File2 or File3 or File4. hence, total ways is actually 4 * (3*2*1*3)

There required prob = 4 * (3*2*1*3) / 3^4 = 8/9 .

(3/3 * 2/3 * 1/3 *3/3)
equals 2/9

This can be done in 4 ways

Hence 8/9