Question

A college professor wants to select three students among twelve students to clean the room. The first student selected will clean the windows, the second student selected will do all the other work, while the third student selected will supervise all activities. In how many different ways can the professor select 3 students form this group.

Answer 1

A college professor wants to select 3 students among 12 students to clean the room.

The first student selected will clean the windows; the second will do all the other work; the thirs student will supervise all activities.

We have to find the different number of ways, in which the professor can select 3 students from the group.

Now, the first student can be selected from the 12 students; so there are 12 options of selecting a boy and then assign him for cleaning windows.

Now, the second student can be selected from the 11 student remaining; so there are 11 options of selecting a student and then assign him to do all the other works.

And finally, the third student can be selected from the rest 10 students remaining; so there are 10 options of selecting a student  and then assign him or her to supervise.

Now, all these three selections are independent of each other.

So, by the multiplication rule of combination,

The total number of ways in which these 3 students could be selected is

=12*11*10

=1320

The answer is

The professor can select 3 students from these group, in 1320 ways.