Permutations (1 Viewer)

[zeek]

In how many ways can 4 people be accomodated into 4 rooms?

 

[Riviet]

I hate these slightly ambiguous questions.

My head always gets flooded with thoughts like:

"Are the rooms identical?"

"Do the rooms fit 4 people?"

My answer: 4⁴ ways if the rooms are distinguishable.

 

[zeek]

yes thats the answer but why?
I assumed that each room would house one person .: there'd be 4! arrangements but apparently this isn't the case.

 

[SoulSearcher]

Because you can have 2 people in one room, 3 people in one room and so on.

 

[zeek]

ohhhhhhhhhhhhhhhhh

so then it would be 1!x2!x3!x4!... but that doesn't equal 4⁴

 

[Riviet]

This is a good way to think of it:

* For the first person to be allocated into a room, there are 4 possible rooms to choose from.

* For the second person to be allocated into a room, there are 4 possible rooms to choose from.

* For the third person to be allocated into a room, there are 4 possible rooms to choose from.

* For the fourth person to be allocated into a room, there are 4 possible rooms to choose from.

.'. number of ways = 4.4.4.4 = 4⁴ or 256.

 

[zeek]

ahhhhhhhhhhhhhh sweet man thx