Question

A committee has

fivefive

members. There are

threethree

members that currently serve as the​ board's

chairman commachairman,

vice chairman commavice chairman,

andand

treasurertreasurer.

Each member is equally likely to serve in any of the positions.

ThreeThree

members are randomly selected and assigned to be the new

chairman commachairman,

vice chairman commavice chairman,

andand

treasurertreasurer.

What is the probability of randomly selecting the

threethree

members who currently hold the positions of

chairman commachairman,

vice chairman commavice chairman,

andand

treasurertreasurer

and reassigning them to their current​ positions?

Answer 1

5 people can be assigned to the three positions in ways.

[JUSTIFICATION: Let first assign to the chairman's post. so we have 5 options for this.

next we assign one of the 4 remaining to the vice chairmans post

and finally assign one of the 3 people left to the post of tressurer. So, we have options]

Now, out of these 60 options, in only one case,( which is unique combination) the three people will be assigned to their previous post.

So, required probability = 1/60

If you have doubts, let me know below.