Probability of going into a room randomly There are 6 different rooms and 3 persons. Every person chooses a random room blindfolded. a) What is the probability that all of them go to different rooms? b) what is the probability that they go to the same room?

a) Is it wrong to say that there is a total number of 6*5*4 = 120 ways that this can happen? person 1 has 6 choices, person 2 has 5 choices, person 3 4 choices. Or rather 6^3 = 216?

b) Would it be right to say since there are 6 rooms, so there is only 6 different ways to pick. so P = 6/216?

I am a bit confused here. Can somebody clear this up please and the above question?

Thanks
Probability here can be found by finding the number of different ways your event can occur and dividing by total number of possible outcomes, which is $6^3=216$.

You are right, for (a), the number of ways this can happen is $6 \times 5 \times 4$ -- now compute the relevant probability.

For (b), there is obviously exactly 6 ways this can happen. Can you compute the probability here as well?
Probability here can be found by finding the number of different ways your event can occur and dividing by total number of possible outcomes, which is $6^3=216$.

You are right, for (a), the number of ways this can happen is $6 \times 5 \times 4$ -- now compute the relevant probability.

For (b), there is obviously exactly 6 ways this can happen. Can you compute the probability here as well?