Can someone explain this question please? (1 Viewer)

[Hehehe22]

I'm new to perms and combs and this is already confusing. Apparently the answer's 4^4 but I don't get why you don't need to account for double-ups? Explanations appreciated

 

[C2H6O]

There's four unique ppl, A, B, C and D. They can go in four unique rooms, 1, 2, 3 and 4, each with four beds. We wanna find out how many ways to assign each person a room, and multiple ppl can have the same room. For example, A1, B1, C2, D3. Start by assigning A a room. There are 4 rooms avaliable (all vacant). Assign B a room. There are still 4 rooms (all rooms have space). Assign C a room. There are still 4 rooms. Assign D a room. There are still 4 rooms. That gives 4*4*4*4=4^4 ways to assign rooms to the four ppl.

 

[Hehehe22]

There's four unique ppl, A, B, C and D. They can go in four unique rooms, 1, 2, 3 and 4, each with four beds. We wanna find out how many ways to assign each person a room, and multiple ppl can have the same room. For example, A1, B1, C2, D3. Start by assigning A a room. There are 4 rooms avaliable (all vacant). Assign B a room. There are still 4 rooms (all rooms have space). Assign C a room. There are still 4 rooms. Assign D a room. There are still 4 rooms. That gives 4*4*4*4=4^4 ways to assign rooms to the four ppl.

Ohhhh ok I think I get it now, thanks
I think I was assuming that each bed was also an option too

 

[ivanradoszyce]

Here is the way that might make it easier to understand. You have 4 rooms, OK, so draw 4 small squares. Ask yourself the question. 'How many choices (or people) can i select to occupy the first room? '. The answer is 4, so place a 4 in the first square. Moving to the next room (or square). Ask yourself the question. 'How many choices (or people) can i select to occupy the second room?' Since each room has enough beds for all the 4 people, place a 4 in the next square. Repeat this process for room 3 and 4. Using the multiplication principle we have:

 

[Hehehe22]

Here is the way that might make it easier to understand. You have 4 rooms, OK, so draw 4 small squares. Ask yourself the question. 'How many choices (or people) can i select to occupy the first room? '. The answer is 4, so place a 4 in the first square. Moving to the next room (or square). Ask yourself the question. 'How many choices (or people) can i select to occupy the second room?' Since each room has enough beds for all the 4 people, place a 4 in the next square. Repeat this process for room 3 and 4. Using the multiplication principle we have:

Thank you! That makes things very clear