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How many ways can you arrange 3 books on one shelf?
Choose 3 then 2 then 1; 3*2*1 = 6 ways.
How many ways can you arrange 6 out of 8 books on a shelf?
Ill skip the factorials and just give you what the calculator does in the end. 8*7*6*5*4*3= 20,160
How many sets of 5 books can be selected from 12 different books?
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.
How many different ways can three books be lined up on a shelf?
6 ways
How many ways can you arrange 2 books on a boos shelf?
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.
