Question

Maizie has the first six books of the little house on the prairie series by laura ingalls wilder arranged in order on the bookshelf. Her mischievous younger brother calvin rearranges all the books into a random order. a) how many possible arrangements of the books are there? b) how much entropy did calvin create in messing up the order of the book?

Answer 1

As there are six books and Maizie's younger brother has only rearranged the books not shifting their position to another location so we can say that Calvin has only the books within the six positions. Now if we fix the position of 1st book then the 2nd book can be put in the rest 5 positions fixing both 1 st and 2 nd book the 3rd book can be put in 4 different position A Again fixing position of 1st three books the 4th book can be kept in 3 different position and similarly fixing the first four books the 5th book can be put in 2 different portion The Last book will be put in the last \r\n empty position This phenomena can happen for all the six books. So there will be (6 times 5 times 4 times 3 times 2 times 1) or '6!' Possible ways to arrange the books in total Total 6! = 720 Possible ways.