## Problems on different ways of Letter arrangement questions and answers

Now

We try to bring together all types of shortcut methods on Letters arrangement for every topic here in this website. Now you just need to apply those tricks to solve these questions. These questions can be solvable without using any shortcut methods also.

Few question on different ways of Letter arrangement will be discuss here. All you need to do is to read the question very carefully and try to solve it by yourself. Answer of this question will be provided along with examples. If you do this problem then check the solution of this question with your answer. If you don’t know how to solve this then also check below.

Every page of this section is contain a question on different ways of Letter arrangement with its detail explanation. Next/Previous link will help you to navigate through other questions. Let’s starts the Question Answer session.

### Example #1

In how many different ways can the letters of the word “STUDENT” be arranged?

- 3060
- 4020
- 5040
- 6080

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (C)

**How to Solve**

Total ways of arrangements is,

STUDENT = 7!

= 7 x 6 x 5 x 4 x 3 x 2 x 1

= 5040.

**Rough Workspace**

### Example #2

In how many different ways can the letters of the word “APPLE” be arranged?

- 120
- 140
- 160
- 180

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (A)

**How to Solve**

Total ways of arrangements is,

APPLE = 5!

= 5 x 4 x 3 x 2 x 1

= 120.

**Rough Workspace**

### Example #3

In how many different ways can the letters of the word “LEARNER” be arranged?

- 2020
- 3080
- 4020
- 5040

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (D)

**How to Solve**

Total ways of arrangements is,

LEARNER = 7!

= 7 x 6 x 5 x 4 x 3 x 2 x 1

= 5040.

**Rough Workspace**

### Example #4

In how many different ways can the letters of the word “DANGER” be arranged?

- 440
- 580
- 640
- 720

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (D)

**How to Solve**

Total ways of arrangements is,

DANGER = 6!

= 6 X 5 X 4 X 3 X 2 X 1

= 720.

**Rough Workspace**

### Example #5

In how many different ways can the letters of the word “LAPTOP” be arranged?

- 660
- 720
- 840
- 980

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (B)

**How to Solve**

Total ways of arrangements is,

LAPTOP = 6!

= 6 X 5 X 4 X 3 X 2 X 1

= 720.

**Rough Workspace**

### Example #6

In how many different ways can the letters of the word “INDIA” be arranged?

- 120
- 180
- 220
- 240

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (A)

**How to Solve**

Total ways of arrangements is,

INDIA = 5!

= 5 X 4 X 3 X 2 X 1

= 120.

**Rough Workspace**

### Example #7

In how many different ways can the letters of the word “BOLLYWOOD” be arranged?

- 335640
- 347820
- 358860
- 362880

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (D)

**How to Solve**

Total ways of arrangements is,

BOLLYWOOD = 9!

= 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1

= 362880.

**Rough Workspace**

### Example #8

How many different ways can be formed by using all the letters of the words “FEBRUARY” so that the vowels always come together?

- 3560
- 4320
- 5880
- 6340

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (B)

**How to Solve**

The word FEBRUARY contains 8 letters.

In this word vowel letters are “EUA”, and we consider it as one single letter.

So, letter be arrange as FBRRY (EUA).

We can arrange 6 letters as ^{6}P_{6}

= 6!

= 6 x 5 x 4 x 3 x 2 x 1

= 720 ways.

We can also arrange 3 vowel as,

= 3!

= 3 x 2 x 1

= 6 ways.

So, required number of arrangements are,

= (720 x 6)

= 4320 ways.

**Rough Workspace**

### Example #9

How many different ways can be formed by using all the letters of the words “COMPUTER” so that the vowels always come together?

- 2240
- 3260
- 4320
- 5780

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (C)

**How to Solve**

The word COMPUTER contains 8 letters.

In this word vowel letters are “OUE”, and we consider it as one single letter.

So, letter be arrange as CMPTR (OUE).

We can arrange 6 letters as ^{6}P_{6}

= 6!

= 6 x 5 x 4 x 3 x 2 x 1

= 720 ways.

We can also arrange 3 vowel as,

= 3!

= 3 x 2 x 1

= 6 ways.

So, required number of arrangements are,

= (720 x 6)

= 4320 ways.

**Rough Workspace**

### Example #10

How many different ways can be formed by using all the letters of the words “SISTER” so that the vowels always come together?

- 240
- 280
- 320
- 360

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (A)

**How to Solve**

The word SISTER contains 6 letters.

In this word vowel letters are “IE”, and we consider it as one single letter.

So, letter be arrange as SSTR (IE).

We can arrange 5 letters as ^{5}P_{5}

= 5!

= 5 x 4 x 3 x 2 x 1

= 120 ways.

We can also arrange 2 vowel as,

= 2!

= 2×1

= 2 ways.

So, required number of arrangements are,

= (120 x 2)

= 240 ways.

**Rough Workspace**

### Example #11

How many different ways can be formed by using all the letters of the words “KEYBOARD” so that the vowels always come together?

- 3440
- 4320
- 5460
- 6580

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (B)

**How to Solve**

The word KEYBOARD contains 8 letters.

In this word vowel letters are “EOA”, and we consider it as one single letter.

So, letter be arrange as KYBRD (EOA).

We can arrange 6 letters as ^{6}P_{6}

= 6!

= 6 x 5 x 4 x 3 x 2 x 1

= 720 ways.

We can also arrange 3 vowel as,

= 3!

= 3 x 2 x 1

= 6 ways.

So, required number of arrangements are,

= (720 x 6)

= 4320 ways.

**Rough Workspace**

Answer of this question is provided along with this examples. Scroll down to see the answer. You can take as much time as you need to answer the question. But try to solve this as quicker as you can.

Please visit this page to get updates on different ways of Letter arrangement. And for more visit Math Shortcut Tricks. You can also like our facebook page to get updates.Few questions on some other topics are also provided here. Click on the Next and Previous link to get few more questions and answers.

If you have any question regarding different ways of Letter arrangement, then please do comment on below section.You can also send us message on facebook.

Please explain Letter

LEARNER

please say me the different arrangement of letters solutions because i just confused in that……..

the solution given is without repitation.if you want with repitation you have to divide with factorial(each repited character)

send me ur no i will sent a no of tricks to u

i find it awsme

i watched your lessons in youtube i liked so….

great a part of ur

i likes this site and helpful to my home preparation.and u send me new trick my email id for my preparation.

Sir You can increase the content with different models

there are many models except these.

Problem 1 . STUDENT

T comes twice so

S-1!

T-2!

U-1!

D-1!

E-1!

N-1!

7!/2!

7x6x5x4x3x2x1

——————–

2×1

=7x6x5x4x3 -> 2520