There are
24 ways
to arrange the 4 items on a bookshelf.
How many different ways can 4 books be selected from a pile of 8 different books and arranged on a shelf?
There are a total of 8! =
40320 ways
of arranging those eight books. First, we consider the case when the two English books are next to each other.
How many ways can 5 books be arranged on a shelf?
See it? Whoa, dude! That’s 5! So, there are
120 ways
to arrange five books on a bookshelf.
How many ways can you arrange 4 books out of 7 books on a shelf?
The dividers must fill each of the remaining six positions. Hence, there are
(104)4! ways
to arrange four distinct books on seven shelves.
How many different ways can you arrange 3 books on a shelf?
different bundles of novels, and we have to put this bundle and other 3 books onto the shelf. So the total number of ways is 3! × (3 + 1)! =
144
.
How many ways can 10 books be arranged on a shelf?
ways. arranged in 9P2 ways. ∴ hence the total number of arrangements =
8! x 9P2 ways
.
How many ways can 5 things be arranged?
So we say that there are 5 factorial = 5! = 5x4x3x2x1 =
120 ways
to arrange five objects.
How many ways can 6 books be arranged on a shelf taken 2 at a time?
For 6 books, that means we have 6 spots to put them in. Our first book has 6 spots it can be in. Our second book will now have 5 , since one is taken up by the first spot. Therefore, we have
720 ways
of arranging 6 books on the shelf.
How many ways can 4 items be arranged?
So, the permutations have 6 times as many possibilites. (Another example: 4 things can be placed in 4! = 4 × 3 × 2 × 1 =
24 different ways
, try it for yourself!)
How many ways can 3 books be arranged on a shelf if they are selected from 6 books?
different bundles of novels, and we have to put this bundle and other 3 books onto the shelf. So the total number of ways is 3! × (3 + 1)! =
144
.
How many ways can 12 books be arranged 3 at a time?
1a) In how many ways can 12 different books be distributed among 3 persons? Solution: There are 3 choices for each of 12 books. The answer is
312
.
How many different ways can 12 different items be arranged on a shelf?
Total number of Ways =
9
!
How many ways can 10 items be arranged?
=
86400 ways
. Let O and E be the odd and even numbers respectively.
How many ways can 10 students can be arranged in a row?
=
3265920 ways
for the ten people to be seated so that a certain to are not next to each other.
How many different ways can 10 books be arranged on a bookshelf if there is only room for 4 books at a time?
ways. ∴ hence the total number of arrangements =
9
!
