Dormitory Requirements for Students

Six students need to be placed in a dormitory. There are four double rooms, two single rooms, and two students cannot be placed together, how many ways are there to place the students?

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...<br>It is same as we get from 4C2 = 4!/2! = 12.
<br>In Lemma 1 if n = m then the formula is ncn = n!/(n-n)! = n!/0! =n!
<br> (Note: 0! = 1)
<br>If there k locations are same and cant be differentiated then the number ways decrease by k! factorial ways.
<br>In the above example say if we cant differentiate between the two places i.e., if cant differentiate between ab and ba
<br>then the number ways decreases by a factor of 2! = 2 and the number ways the ...