From 6 different novels and 3 different dictionaries,4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle ,then find the number of such an arrangement?

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Answer 1 · 2018-04-02T15:26:22

1080 ways

We're picking 5 books in total. The dictionary will be the middle book so let's look at that first.

There are 3 different dictionaries to pick from, and so the number of choices for that middle book is 3.

The remaining 4 spots for books will be chosen from a population of 6. We can use the permutation formula #(P_(6,4)=(6!)/(2!)=6xx5xx4xx3=360)#.

All told, there is #3xx360=1080# ways to arrange the books.