Ten students need to be assigned dormitory rooms. There are 8 available rooms, and a maximum of 2 students can occupy each room. How many ways can the students be assigned if exactly two rooms are to be left empty?

Question

Ten students need to be assigned dormitory rooms.  There are 8 available rooms, and a maximum of 2 students can occupy each room. How many ways can the students be assigned if exactly two rooms are to be left empty?

anonymous · Answer

8 C 2

anonymous · Answer

28ways

lgbasallote · Answer

it's not that simple...

anonymous · Answer

Is 28 wrong?

lgbasallote · Answer

yes

anonymous · Answer

I selected two from the eight rooms which needs to be empty and selected o students from ten as they need to be empty.
(8 C 2) x (10 C 0) = 28
So, this is wrong..okay i'll try in another way

anonymous · Answer

permutations,combinations and probability are always fun!!

lgbasallote · Answer

...what you did was the way of selecting the empty rooms...right?

anonymous · Answer

yea...

lgbasallote · Answer

but the question is ways of assigning the students...

anonymous · Answer

yes i got that while thinking for the second time..

anonymous · Answer

8C6 * 10C2 * 8C2 * 6C2 * 4C2 * 6!

anonymous · Answer

8C2*10C6*6!*8C4*4!

anonymous · Answer

Sorry the first term is 8C6

anonymous · Answer

Yes but to understand it clearly I thought this would be easy

lgbasallote · Answer

it's not easy

anonymous · Answer

Its wrong again?!

lgbasallote · Answer

and i have no idea what @sauravshakya did

anonymous · Answer

If that is not the correct answer.... Then there is no meaning explaining it.

lgbasallote · Answer

yeah neither one of those is

anonymous · Answer

Isnt it 8P6 * 10C2 * 8C2 * 6C2 * 4C2

anonymous · Answer

Did I miss something?

lgbasallote · Answer

you did...since that's a big number

anonymous · Answer

Yeah that is a very big number

anonymous · Answer

7112448000

lgbasallote · Answer

very very

lgbasallote · Answer

but anyway...why give answers before solutions?

anonymous · Answer

I calculated the solution I gave..that's it..This is not another answer

anonymous · Answer

8C6*10C6*6!*6C4*4!

lgbasallote · Answer

i was referring to saurav

anonymous · Answer

Just a bit of change to my previous answer..8C4 is replaced by 6C4

anonymous · Answer

Is my answer correct now.....the number i get is 1524096000

lgbasallote · Answer

not really..no...

lgbasallote · Answer

what are you doing anyway? how are you getting those numbers?

anonymous · Answer

First select any 6 rooms from 8 (8C6). then select 6 students from 10 (10C6) and arrange them in 6rooms (6!). Now select any 4 rooms from the 6 rooms selected previously (6C4) and arrange the remaining 4 students in these 4 rooms in 4! ways.

lgbasallote · Answer

..but you did not consider the order did you?

anonymous · Answer

What order?

lgbasallote · Answer

the order of the rooms

lgbasallote · Answer

where the empty ones are; where the room with one student are; where the room with the two studets are

anonymous · Answer

I didn't understand the need to do that..

lgbasallote · Answer

because each room is distinct...

lgbasallote · Answer

one room can either be empty/one student/two students... so order should be considered

anonymous · Answer

If somehow I correct it this way,is this correct
8P6*10P6*8P4*4!*8P2

experimentx · Answer

kinda looks like 
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but we have to consider 12<-->21 symmetry ... i guess. tricky Q