Question

There are 10 books are arranged on a shelf. If 4 books you are choosing are in alphabetical order,how many different groups of books could be chosen? Determine if it is permutation orcombination then solve.A). 24B). 210C). 3,628,800D). 5040

Answer 1

The problem says you have 10 books arranged on a shelf and then you are choosing 4 books in alphabetical order.

Given that you are choosing books with an order (alphabetical) it means the order does matter, then it is a permutation (which is an ordered combination).

In this case, no repetitions are allowed because you can't repeat a book in the selection, they'll be 4 different books from the shelf, the formula you have to use is:

`(n!)/((n-r)!)\begin{cases}n=\text{total number of books} \\ r=\text{ number of books you are choosing}\end{cases}`

Then n=10 and r=4, replace these values:

`(10!)/((10-4)!)=(3628800)/(720)=5040`

Then, can be chosen 5040 different groups of books.

The answer is option D.