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Ill skip the factorials and just give you what the calculator does in the end.

8*7*6*5*4*3=

20,160

Q: How many ways can you arrange 6 out of 8 books on a shelf?

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asdasdadadadasdasd

Choose 3 then 2 then 1; 3*2*1 = 6 ways.

12!/(5!*7!)The number of ways to arrange nitems is n!, where "!" is the factorial function. The number of ways we can arrange the 12 books is therefore 12!. However, we don't really care what order the first 5 books are in, or what order the last 7 books are in, as long as they're the same books. We therefore divide by the number of ways to arrange 5 books and the number of ways to arrange 7 books.

6 ways

2. If the books are x and y, then xy or yx are the only possible ways. Unless you allow for one book to the side of the other, one bok on top of the other, one book leaning partially on the other, etc. In that case, there are an infinite number of ways.

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asdasdadadadasdasd

30 ways.

The answer to this one is 24. You can do this mathematically by 4*3*2*1.

Choose 3 then 2 then 1; 3*2*1 = 6 ways.

The answer would be 7! or (7*6*5*4*3*2*1)=5040

5 books can be lined up on a shelf in (5 x 4 x 3 x 2 x 1) = 120 different sequences.

Yes. They are real.

120. You do 5*4*3*2*1=120. you multiply the number that you are given for example how many times can books 3 be arranged on a shelf you multiply 3*2*1=6 that is your answer

10!

There are only 5 places on the shelf. You have 7 books to choose from. We will ignore the order of the books on the shelf. The first place can be filled from a choice of 7 books, the next place from 6, the next place from 5, the next from 4, and the last of the 5 places from 3 books. So the number of ways of choosing the 5 is found from 7 * 6 * 5 * 4 * 3 = 2520

You can wind up with 10 different pairs of books in your hand, which you can choose from a shelf of 5 books in 20 different ways.

it depends on the shelf of course