If the librarian follows a standard scheme, such as the Dewey Decimal, then there is essentially only one way. If the librarian arranged books randomly it would become extremely difficult to find any books: the library would become unusable and the librarian would get sacked. So again not many ways of arranging books before you stop being a librarian.
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10!
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.
30 ways.
To arrange 3 algebra books and 3 geometry books on a shelf so that no two books of the same type are next to each other, you can use the concept of permutations. There are 3! ways to arrange the algebra books and 3! ways to arrange the geometry books. This gives a total of 3! * 3! = 36 ways to arrange the books on the shelf such that no two books of the same type are next to each other.
Choose 3 then 2 then 1; 3*2*1 = 6 ways.
The answer to this one is 24. You can do this mathematically by 4*3*2*1.
Approx 257 quadrillion ways.
There are 40! arrangements of all 40 books. To find the arrangements where two Hindi books are together, consider them as one unit. There are 20! ways to arrange this combined unit along with the other books. Then, within this unit, there are 2! ways to arrange the two Hindi books. So, the total number of ways where two Hindi books are together is 20! * 2!. Subtract this from 40! to find the total number of ways where two Hindi books are not together.
Yes. They are real.
you can arrange three beads 9 different ways.
you can arrange 8 pictures 28 different ways