Here's another fun one! Fifteen students are distributed to three classes. Anong them, three of them are special students. What are the probability that each class has only one special student?

Question

anonymous · Answer

$$\frac{ (potato-1)! }{ potato!(potato-2)! }$$

anonymous · Answer

Potatoes!! lol

anonymous · Answer

3! * 3^12

anonymous · Answer

Isn't that larger than 1?

anonymous · Answer

Oh sorry that was number of ways it can be done.

anonymous · Answer

(3! * 3^12)/3^15

anonymous · Answer

The students can only be shuffled within their respective classrooms though...

anonymous · Answer

And that means?

anonymous · Answer

that means that once a special occupies a classroom, the other students might lose that chance to go into that classroom for the the probability that one student goes into one classroom.

anonymous · Answer

What was wrong with the answer I gave?

anonymous · Answer

your students were given three choices no matter the permutations of the three specials. however, in the case of two specials occupying two classrooms, they would only have one choice instead.

anonymous · Answer

First special student have 3 choices
Second special student have 2 choices
Third special student have one choices.
And  the rest students will have 3 choices.

anonymous · Answer

yes. 
But in the case of 1-1-13 classroom arrangement, where the first two classes will have the two specials, the 12 students don't have this choice of entering the classroom.

anonymous · Answer

@Shadowys  can u PLZ explain the question once again.

anonymous · Answer

sorry~ ehheh
Fifteen students,  three among them are special. are distributed to three classes, and each class must contain only one special student, there is no limit on the number of students in the class except that all students must go into a class. What is the probability?

anonymous · Answer

Then, what is wrong with 3!*3^12/3^15

anonymous · Answer

the students can be reshuffled in the classes without changing the class.
 Frankly saying, I got your answer when I first did it before I tried simplifying the question and testing it again. Hmm~I'll check with teacher again. It might be that he's wrong~

anonymous · Answer

@satellite73  PLZ check this.

anonymous · Answer

i don't understand the question

anonymous · Answer

Oh my. Is it that vague?