Barron's 2400, Permutations & Combinations

Test Preparation
1

Can somebody provide me with a good explanation on the difference between permutations and combinations? One question in Barron’s is: Rachel is hanging posters in her new apartment, which includes a bedroom, a living room, and a den. She has 7 different posters. Assuming that she plans to place exactly 1 poster in each of the 3 rooms, how many choices does she have?
Answer from the book: 7x6x5= 210 choices

However, the book also states that when the order of arrangement does not matter, you treat it as a combination. Thus isn’t it wrong to treat it as a “permutation” in this case because the order in which the posters are arranged in the rooms does not matter?

2

I’d be careful here - the rooms are different, so placing poster A, B, C in the bedroom, living room, and den, respectively, is different from placing posters C, A, B respectively or any of the other rearrangements. Or, you could assume without loss of generality that the first poster selected goes in the bedroom, the second goes in the living room and the third goes in the den, in which order matters here.

On the other hand, if it was asking for the number of ways to select any three posters without regards to order, then the number of ways is 7C3 = 35.