Problems on different ways of Letter arrangement questions and answers

Now here we will discuss few question answers on different ways of Letter arrangement which are very common in competitive exams. These Letters arrangement practice question answer session will help you to prepare for your examination. Your math skills is very much needed to solve this kind of problems. Shortcut tricks can also be used to solve different ways of Letter arrangement questions.

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.

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Example #1 – Different ways of Letter arrangement

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

3060

4020

5040

6080

Show AnswerShow How to SolveOpen 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 – Different ways of Letter arrangement

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

120

140

160

180

Show AnswerShow How to SolveOpen 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 – Different ways of Letter arrangement

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

2020

3080

4020

5040

Show AnswerShow How to SolveOpen 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 – Different ways of Letter arrangement

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

440

580

640

720

Show AnswerShow How to SolveOpen 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 – Different ways of Letter arrangement

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

660

720

840

980

Show AnswerShow How to SolveOpen 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 – Different ways of Letter arrangement

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

120

180

220

240

Show AnswerShow How to SolveOpen 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 AnswerShow How to SolveOpen 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 AnswerShow How to SolveOpen 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} or, 6! or, 6 x 5 x 4 x 3 x 2 x 1 therefore, 720 ways.

We can also arrange 3 vowel as, or, 3! or, 3 x 2 x 1 therefore, 6 ways.

So, required number of arrangements are, or, (720 x 6) therefore, 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 AnswerShow How to SolveOpen 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} or, 6! or, 6 x 5 x 4 x 3 x 2 x 1 therefore, 720 ways.

We can also arrange 3 vowel as, or, 3! or, 3 x 2 x 1 therefore, 6 ways.

So, required number of arrangements are, or, (720 x 6) therefore, 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 AnswerShow How to SolveOpen 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} or, 5! or, 5 x 4 x 3 x 2 x 1 therefore, 120 ways.

We can also arrange 2 vowel as, or, 2! or, 2×1 therefore, 2 ways.

So, required number of arrangements are, or, (120 x 2) therefore, 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 AnswerShow How to SolveOpen 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} or, 6! or, 6 x 5 x 4 x 3 x 2 x 1 therefore, 720 ways.

We can also arrange 3 vowel as, or, 3! or, 3 x 2 x 1 therefore, 6 ways.

So, required number of arrangements are, or, (720 x 6) therefore, 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.

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Please explain Letter

LEARNER

5*4*3*2*1= 120

3*2*1= 6

120*6= 720

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