# Dormitory Requirements for Students

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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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Little theory before going to the solution

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<br>If there are n different items and m items have to be arranged then it can be done in nCm ways nCm= n!/(n-m)!

<br>where n! = n * (n-1) * (n-2) ...* 1 -----Lemma 1

<br>for example 4! = 4 * 3 * 2 *1

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<br>An example for above statement say there 4 letters a,b,c,d

<br>Different ways in which you can arrange 2 letters are

<br> ab, ac, ad, bc, bd, cd, dc, db, bc, da, ca, ba

<br>So, no ways we can arrange is ...

#### Solution Summary

The expert examines dormitory requirements for students.

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