PROBABILTY Question (1 Viewer)

[sleepyair]

A motel has 4 rooms that can fit 4 people each. How many ways can 6 people be arranged in these rooms?

 

[braintic]

A motel has 4 rooms that can fit 4 people each. How many ways can 6 people be arranged in these rooms?

First distribute the 6 people any which way: 4^6 possibilities

Then take away the number of ways they could all be in the same room: 4

And finally take away the number of ways that exactly 5 could be in the same room:
4 possibilities for the room containing 5 people
3 possibilities for the other room used
6 possibilities for the odd man out (which automatically selects the group of 5)

So I believe the answer is 4^6 - 4 - 4*3*6 = 4020

Does that match the answer you have?

 

[sleepyair]

I don't get how they could all be in the same room. 1 room=4 people, how can 6 people be in a room? :/

The answer is 4020.

 

[Carrotsticks]

I don't get how they could all be in the same room. 1 room=4 people, how can 6 people be in a room? :/

The answer is 4020.

Exactly, we are subtracting those possibilities from the total so then we can fit the condition that 1 room = 4 people.

 

[sleepyair]

I GET IT. Thanks braintic and Carrotsticks!

 

[Squar3root]

reminds me from the 2013 mx2 hsc paper. it was a m/c question lol