SOLUTION: There are 100 students that are randomly placed into 4 classrooms. Three students want to be in the same class. Probability they are in the same class? probability they are all P's

Question 245300: There are 100 students that are randomly placed into 4 classrooms. Three students want to be in the same class. Probability they are in the same class? probability they are all P's class? Probability they are all in different classes?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
There are 100 students that are randomly placed into 4 classrooms.
Three students want to be in the same class.
----------------------------------------------
Probability they are in the same class?
Pick a classroom: 4 ways
Place the 3 randomly: 100*99*98 ways
Probability 4/(100*99*98) = 0.000004123
---------------------------------------------
probability they are all in P's class?
# of ways to succeed: 1 way
# of ways to place randomly: 100*99*98
Probability = 1/970200
=============================================
Probability they are all in different classes?
Pick 3 classes: 4C3 = 4
Put the 3 students in the three classes: 3*2*1 = 6
probability (4*6)/970200 = 0.00002474
========================================
Cheers,
Stan H.

RELATED QUESTIONS
A student is looking for history class and knows he must be in one of nine classrooms.... (answered by ewatrrr)

There are 100 students overall, and they are distributed into 4 classrooms of equal size. (answered by stanbon)

Can you provide more detail on the answers provided to question 245824 from stanbon:... (answered by nyc_function)

There are 100 students in the senior class. How many ways can 6 students be chosen to... (answered by Edwin McCravy)

There are 25 students in a class, 15 male and 10 female. The teacher randomly selects... (answered by John10)

3) A class has 28 students. There are 5 good students, 13 fairly good students and 10... (answered by Edwin McCravy)

A class has 28 students. There are 5 good students, 13 fairly good students and 10 medium (answered by sudhanshu_kmr)

In a class of 100 students, 40 are left-handed. Using this statement, determine the... (answered by edjones)

There are 12 students in a particular class. Only 4 students are allowed to be in the... (answered by stanbon)