Table of Contents

- 1 How many arrangements of A A A B B B C C C are there such that no three consecutive letters are the same?
- 2 How many permutations are possible using the 6 letters in the word Alaska?
- 3 How many permutations of the letters A to H are there if the three letters a B and C must appear side by side but not necessarily in the order A B C?
- 4 How do you solve permutations?
- 5 How many distinguishable 6 letter words can be formed using the letters banana?
- 6 What is the number of ways to arrange the six letters in the word follow?
- 7 How many different permutations are there of the set Abcde?
- 8 How do you calculate total permutations?

## How many arrangements of A A A B B B C C C are there such that no three consecutive letters are the same?

+(33)3! so the number of arrangements in which no three consecutive letters are identical is 9!

## How many permutations are possible using the 6 letters in the word Alaska?

Since we are treating reflections as distinguishable, there are 20 distinguishable circular permutations of the word ALASKA.

**How many ways can the letters A B B B C C C D D E be arranged?**

Thus, the answer you want is 3360/2=1680. Since in each rearrangement you can then replace the left most X with D and the right most with C you have counted the ways to arrange “A,A,B,B,B,C,D,E” such that C is always somewhere to the right of D.

### How many permutations of the letters A to H are there if the three letters a B and C must appear side by side but not necessarily in the order A B C?

= 4320 arrangements. ABC always appear together.

### How do you solve permutations?

To calculate the number of permutations, take the number of possibilities for each event and then multiply that number by itself X times, where X equals the number of events in the sequence. For example, with four-digit PINs, each digit can range from 0 to 9, giving us 10 possibilities for each digit.

**What is permutation combination?**

Permutation and combination are the ways to represent a group of objects by selecting them in a set and forming subsets. When we select the data or objects from a certain group, it is said to be permutations, whereas the order in which they are represented is called combination.

#### How many distinguishable 6 letter words can be formed using the letters banana?

which gives 60 So 60 distinguishable permutation of the letters in BANANA.

#### What is the number of ways to arrange the six letters in the word follow?

720 arrangements

So the six letters can be a combination of 6×5×4×3×2×1 letters or 720 arrangements.

**How many permutations does Abcde have?**

A total of 18+ 18+ 12= 48 permutations.

## How many different permutations are there of the set Abcde?

The set which comprises 7 elements a, b, c, d, e, f, g are to be arranged and this can be done in 7! or 5040 ways.