30 ways.
5 books can be lined up on a shelf in (5 x 4 x 3 x 2 x 1) = 120 different sequences.
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
There are 40320 ways.
The answer depends on how many books on each subject there are.
Consider one placement at a time. The first book on the shelf could be any of seven. The second could be any of the remaining six. This continues with the rest. The total combinations are: 7! = 7*6*5*4*3*2*1 = 5040
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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.
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.
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.
The answer would be 7! or (7*6*5*4*3*2*1)=5040
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
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
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.
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.
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.