Contents

- 1 How many different ways can 4 math books and 5 other books be arranged on a shelf if the math books are kept together?
- 2 How many ways can 4 books be arranged on a shelf?
- 3 How many ways can 5 books be arranged?
- 4 How many ways can you arrange 4 out of 7 books on a shelf?
- 5 How many ways can 9 books be arranged on a shelf?
- 6 How many ways can 8 books be arranged on a shelf?
- 7 How many ways can you arrange 4 things?
- 8 How many 4 book selections are there?
- 9 How many different teams of 4 students could be chosen from the 15 students?
- 10 How many ways can you arrange 6 things?
- 11 How many ways can 9 things be arranged?
- 12 How many ways can 12 books be arranged 3 at a time?
- 13 How many ways can 12 swimmers finish in first second and third place?
- 14 How many ways can 10 books be arranged on a shelf?
- 15 How many ways can 7 numbers be arranged?

## How many different ways can 4 math books and 5 other books be arranged on a shelf if the math books are kept together?

For the 5 math books: 5 ∗ 4 ∗3∗2∗1= 5! ways to arrange them, or 120. For the 4 novels: 4 ∗3∗2∗1= 4!$ ways to arrange them, or 24.

## How many ways can 4 books be arranged on a shelf?

There are 24 ways to arrange the 4 items on a bookshelf.

## How many ways can 5 books be arranged?

So, there are 120 ways to arrange five books on a bookshelf.

## How many ways can you arrange 4 out of 7 books on a shelf?

The dividers must fill each of the remaining six positions. Hence, there are (10 4 ) 4! ways to arrange four distinct books on seven shelves.

## How many ways can 9 books be arranged on a shelf?

So for each of the possible 40320 ways to arrange the other 8 books, there are 2 possible acceptable arrangements of 9 books.

## How many ways can 8 books be arranged on a shelf?

Therefore, 8 books could be arranged in 40,320 ways.

## How many ways can you arrange 4 things?

But many of those are the same to us now, because we don’t care what order! 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 4 book selections are there?

Answer: Since there are 10 different books out of which 4 is to be selected.

## How many different teams of 4 students could be chosen from the 15 students?

How many different committees of 4 students can be chosen from a group of 15? Answer: There are possible combinations of 4 students from a set of 15. There are 1365 different committees.

## How many ways can you arrange 6 things?

There are 720 ways in which six things can be arranged. Each distinct arrangement is called a permutation. Permutations are computed using factorials.

## How many ways can 9 things be arranged?

362880 is the number of ways to arrange 9 letters (alphabets) word “FRACTIONS” by using Permutations (nPr) formula.

## 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 ways can 12 swimmers finish in first second and third place?

Only one person can win first, second and third place. The total number of placers is 12 times 11 times 10.

## How many ways can 10 books be arranged on a shelf?

arranged in ^{9}P _{2} ways. ∴ hence the total number of arrangements = 8! x ^{9}P _{2} ways.

## How many ways can 7 numbers be arranged?

This can be done `7! = 5040 ` ways.