The question given below is a sample question in Counting Methods and Permutation Combination. This particular question is an example of reordering m things in n places, where m > n
Question 2
In how many ways can 4 boys be assigned to 3 different rooms such that no room is empty?
A.
3C
1* 2!
B.
4C
2* 3C
1
C. 4!
D.
E.
4C
2 * 3!
Correct answer is
4C
2 * 3!. Choice (E).
Explanatory Answer
No room can be empty, so the boys need to be assigned as 2 to a room, 1 to a room and 1 to a room.
There will be exactly one room that has 2 boys in it.
First let us select the two boys who are going to share a room. i.e., we have two select 2 boys out of 4 boys.
This can be done in
4C
2 ways.
Once we have done this, we have to assign rooms to the boys.
We have to assign 3 rooms to 3 sets of boys (1,1 and 2 members in each set).
This can be done in 3! ways.
Therefore, total number of ways =
4C
2 * 3!
