GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Sep 2018, 22:23

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# How many 4-letter words can be formed using the alphabets of the word

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2014
How many 4-letter words can be formed using the alphabets of the word  [#permalink]

### Show Tags

Updated on: 07 Aug 2018, 01:06
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:54) correct 42% (02:04) wrong based on 85 sessions

### HideShow timer Statistics

How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word contains alphabets G and L and repetition of alphabets are not allowed?

A. $$60$$
B. $$120$$
C. $$180$$
D. $$200$$
E. $$240$$

Thanks,
Saquib
Quant Expert
e-GMAT

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Originally posted by EgmatQuantExpert on 30 Jan 2017, 00:33.
Last edited by EgmatQuantExpert on 07 Aug 2018, 01:06, edited 1 time in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2014
Re: How many 4-letter words can be formed using the alphabets of the word  [#permalink]

### Show Tags

Updated on: 30 Jan 2017, 23:12
The official solution has been posted. Looking forward to a healthy discussion..
_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Originally posted by EgmatQuantExpert on 30 Jan 2017, 00:34.
Last edited by EgmatQuantExpert on 30 Jan 2017, 23:12, edited 1 time in total.
Manager
Joined: 21 Jan 2016
Posts: 81
Location: India
GMAT 1: 670 Q50 V30
WE: Engineering (Computer Software)
Re: How many 4-letter words can be formed using the alphabets of the word  [#permalink]

### Show Tags

30 Jan 2017, 08:53
Is answer C ? We need to select 2 alphabets from E,N,I,S and H, which are arranged also, so 5P2 = 20. We have 3 places so total = 20*3*2*1 = 120;
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4033
Location: India
GPA: 3.5
Re: How many 4-letter words can be formed using the alphabets of the word  [#permalink]

### Show Tags

30 Jan 2017, 09:15
1
EgmatQuantExpert wrote:
How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word contains alphabets G and L and repetition of alphabets are not allowed?

A. $$60$$
B. $$120$$
C. $$180$$
D. $$200$$
E. $$240$$

We have here 7 letters ( E,N,G,L,I,S & H )

And 4 places as _ _ _ _

G & L must be there, so we can arrange the 2 letters in 2! or 2 ways and the next 5 Letters ( E,N,I,S & H ) in 2 places in 5! ways ie, 120 ways...

So, Total Number of ways is 120*2 = 240 ways..

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Math Expert
Joined: 02 Aug 2009
Posts: 6808
Re: How many 4-letter words can be formed using the alphabets of the word  [#permalink]

### Show Tags

30 Jan 2017, 09:33
3
EgmatQuantExpert wrote:
How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word contains alphabets G and L and repetition of alphabets are not allowed?

A. $$60$$
B. $$120$$
C. $$180$$
D. $$200$$
E. $$240$$

Thanks,
Saquib
Quant Expert
e-GMAT

Hi ankujgupta
Do not start arranging the alphabets before selection.
Total 7 letters out of which 4 are to be choosen..
G and L are already there, so choose 2 out of remaining 5.. 5C2=$$\frac{5!}{3!2!}=10$$..

Now 4 letters can be choosen in 10 ways but they can be arranged in 4! Or 4*3*2=24 ways..

Total 10*24=240..
E
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 21 Jan 2016
Posts: 81
Location: India
GMAT 1: 670 Q50 V30
WE: Engineering (Computer Software)
Re: How many 4-letter words can be formed using the alphabets of the word  [#permalink]

### Show Tags

30 Jan 2017, 11:27
chetan2u wrote:
EgmatQuantExpert wrote:
How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word contains alphabets G and L and repetition of alphabets are not allowed?

A. $$60$$
B. $$120$$
C. $$180$$
D. $$200$$
E. $$240$$

Thanks,
Saquib
Quant Expert
e-GMAT

Hi ankujgupta
Do not start arranging the alphabets before selection.
Total 7 letters out of which 4 are to be choosen..
G and L are already there, so choose 2 out of remaining 5.. 5C2=$$\frac{5!}{3!2!}=10$$..

Now 4 letters can be choosen in 10 ways but they can be arranged in 4! Or 4*3*2=24 ways..

Total 10*24=240..
E

chetan2u Thanks. Got the error.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2014
How many 4-letter words can be formed using the alphabets of the word  [#permalink]

### Show Tags

Updated on: 07 Aug 2018, 02:34
Hey,

PFB the official solution.

This question can be done in a number of ways. Let us focus on the two important methods of solving this question –

Method 1 –

Step 1: Understand the objective

The objective of the question is to find the number of 4-letter words that can be formed from the alphabets of the word ENGLISH.

The information given is:

• There are a total of 7 alphabets: E, N, G, L, I, S and H.
• Repetition of letters is not allowed.
• Two letters G and L are to be included necessarily in all the words.
• Per the question, it is not necessary for the word formed to convey a meaning per English dictionary.

So, now we know the objective of the question and the information provided in the question.

Step 2: Write the objective equation enlisting all tasks

The objective comprises of the following tasks:

• Task 1 – Select two letters from the letters G and L. (As these two are to be necessarily included)
• Task 2 – Select two letters from E, N, I, S, and H.
• Task 3 – Form 4-letter words from the four letters that are selected in the previous two tasks.
o Now, in order to accomplish the objective, all the three tasks need to be done. So, in the objective equation, we will put a multiplication sign between the number of ways of doing the three tasks.

The Objective Equation will therefore be:

Step 3: Determine the number of ways of doing each task

• Task 1 is to select two letters from the letters G and L.

o Now, the number of ways to select 2 letters from 2 different letters = 2C2 = 1
o Thus, number of ways to do Task 1 = 1

• Task 2 is to select two letters from the 5 letters E, N, I, S, and H.

o The number of ways to select 2 letters from 5 different letters = 5C2 = 10
o Thus, number of ways to do Task 2 = 10

• Task 3 is to arrange the selected 4 letters in 4 spaces to form different words.

o Now, the number of ways in which 4 letters can be arranged in 4 spaces= 4! = 4 X 3 X 2 X 1
o Thus, number of ways to do Task 3 = 24

Step 4: Calculate the final answer

• In this step, we are going to plug the values in the above equation:
o Number of different 3-letter words = 1 x 10 x 24 = 240
o So, there are 240 words that can be formed per the condition stated in the question.
• Thus, the correct answer choice is Option D.

Thanks,
Saquib
Quant Expert
e-GMAT

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Originally posted by EgmatQuantExpert on 30 Jan 2017, 23:04.
Last edited by EgmatQuantExpert on 07 Aug 2018, 02:34, edited 1 time in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2014
Re: How many 4-letter words can be formed using the alphabets of the word  [#permalink]

### Show Tags

30 Jan 2017, 23:12
1
Method 2 –

• Now let us look at another way to solve this question.
• We need to make 4 -letter words in which G,L must be present .
• And the remaining two spaces must be filled with the remaining 5 letters.
• Thus, the objective equation can be written as

• Thus if we make 4 spaces and try to arrange GL in these 4 spaces, we will clearly see that GL can be arranged in 4P2 ways.
o Thus, the number of ways to arrange GL on 4 spaces = 4P2 = 4!/2! = 12 ways.

• To fill the remaining two spaces, we have 5 letters to choose from and arrange them
o E, N, I, S, H

• Thus, the remaining two spaces can be filled and arranged in = 5P2 = 5!/3! = 20 ways.
• Plugging the two values in the objective equation, we get

o The number of ways to make 4 letter words = 12 x 20 = 240 ways.

• As we can see both the methods give us the same answer. In the first method, we first selected the letters and then arranged them and in the second method, we did the selection and arrangement simultaneously.

Please Note: When we say that G and L must be there in the 4 letter word, it means that they can be placed anywhere in the 4 letter word. And it is NOT necessary to place GL together in the 4 letter word. This is a common mistake, which a lot of students make and one must avoid falling into such a trap!

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Non-Human User
Joined: 09 Sep 2013
Posts: 8177
Re: How many 4-letter words can be formed using the alphabets of the word  [#permalink]

### Show Tags

02 Sep 2018, 00:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: How many 4-letter words can be formed using the alphabets of the word &nbs [#permalink] 02 Sep 2018, 00:42
Display posts from previous: Sort by

# How many 4-letter words can be formed using the alphabets of the word

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.