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?© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/calculus-and-analysis/dormitory-requirements-for-students-2t6
...<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 ...