# Permutaion Or Combimnation ? Then Solve . 6 Books to be arranged on a shelf

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### 3 Answers

You may rearrange the 6 books on the shelf in different ways and you may find the number of permutations using factorial formula such that:

`n! = 1*2*3*...*(n-2)*(n-1)*n`

Hence, reasonign by analogy yields:

`6! = 1*2*3*4*5*6 => 6! = 720`

**Hence, since the problem does not indicate to arrange a given number of books, out of all 6, on the shelf, then you only may solve the problem using permutation `6! = 720` .**

The answer is indeed 6!=720, but those are **permutations**. Combinations would be if you were asked in how many ways can you choose eg. 2 out of 6 books. In that case the answer would be `6 choose 2 = (6 cdot 5)/(1 cdot 2) = 15.`

Note: number of permutations = number of arrangements.

Permutation is an arrangement where the order does not matter. So the answer is

6!=720

Combination is a selection where the order does not matter as well. So the answer is

1 for the 6 books.

But if you choose 3 books from it and ask for the different combinations. It is 20. (6!)/((3!)(3!))= 20. I hope it helps.