It is currently 17 Jan 2018, 10:25

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# From 7 consonants and 5 vowels, how many words can be formed

Author Message
TAGS:

### Hide Tags

Manager
Joined: 24 Oct 2005
Posts: 52

Kudos [?]: 8 [3], given: 0

From 7 consonants and 5 vowels, how many words can be formed [#permalink]

### Show Tags

28 Dec 2005, 18:45
3
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

62% (00:56) correct 38% (00:25) wrong based on 22 sessions

### HideShow timer Statistics

From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.

OA:
[Reveal] Spoiler:
1,764,000

_________________

"The difference between a smart person and a wise person is that
a smart person knows what to say and
a wise person knows whether or not to say it."

Last edited by Bunuel on 23 Nov 2013, 05:18, edited 1 time in total.

Kudos [?]: 8 [3], given: 0

Director
Joined: 09 Oct 2005
Posts: 712

Kudos [?]: 26 [0], given: 0

Re: PS - Probability Consonants & Vowels [#permalink]

### Show Tags

28 Dec 2005, 21:30
1
This post was
BOOKMARKED
Itzrevs wrote:
From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.

Number of ways to choose 4 cons out of 7*Number of ways to choose 3 vowels out of 5---->4C7*3C5=(7*6*5*4/1*2*3*4)*(5*4*3/1*2*3)=350

Kudos [?]: 26 [0], given: 0

Senior Manager
Joined: 14 Apr 2005
Posts: 414

Kudos [?]: 18 [0], given: 0

Location: India, Chennai
Re: PS - Probability Consonants & Vowels [#permalink]

### Show Tags

29 Dec 2005, 00:18
Itzrevs wrote:
From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.

Since the order of the letters are important we get
7P4*5P3 = 4200

Kudos [?]: 18 [0], given: 0

Manager
Joined: 24 Oct 2005
Posts: 52

Kudos [?]: 8 [0], given: 0

### Show Tags

29 Dec 2005, 07:05
sorry guys both of you didn't get the OA..

Lets give it another try
_________________

"The difference between a smart person and a wise person is that
a smart person knows what to say and
a wise person knows whether or not to say it."

Kudos [?]: 8 [0], given: 0

Intern
Joined: 18 Jul 2003
Posts: 12

Kudos [?]: 4 [0], given: 0

### Show Tags

29 Dec 2005, 07:55
4 consonants can be chosen in 7*6*5*4 ways

3 vowels can be chosen in 5*4*3 ways

Total no. of alternatives =7*6*5*4*5*4*3=50,400

Kudos [?]: 4 [0], given: 0

Manager
Joined: 11 Aug 2005
Posts: 82

Kudos [?]: 21 [0], given: 0

Re: PS - Probability Consonants & Vowels [#permalink]

### Show Tags

29 Dec 2005, 09:54
krisrini wrote:
Itzrevs wrote:
From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.

Since the order of the letters are important we get
7P4*5P3 = 4200

u have put the right formula but calculated it incorrectly. ur answer shud also be 50400....
_________________

------------------------------

only if i could choose....

Kudos [?]: 21 [0], given: 0

Manager
Joined: 24 Oct 2005
Posts: 52

Kudos [?]: 8 [0], given: 0

### Show Tags

29 Dec 2005, 20:50
Yurik79, I didn't the same way as you did. But thats not the answer.

I shall wait for few more people to jump in and post their answers & explanations..

Will post the OA soon.
_________________

"The difference between a smart person and a wise person is that
a smart person knows what to say and
a wise person knows whether or not to say it."

Kudos [?]: 8 [0], given: 0

Senior Manager
Joined: 14 Apr 2005
Posts: 414

Kudos [?]: 18 [0], given: 0

Location: India, Chennai
Re: PS - Probability Consonants & Vowels [#permalink]

### Show Tags

29 Dec 2005, 21:22
crazyfin wrote:
krisrini wrote:
Itzrevs wrote:
From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.

Since the order of the letters are important we get
7P4*5P3 = 4200

u have put the right formula but calculated it incorrectly. ur answer shud also be 50400....

Thanks crazyfin. The compuatation should have worked to 50400, I am not sure how I made this mistake, thanks much for pointing out.

Kudos [?]: 18 [0], given: 0

Manager
Joined: 24 Oct 2005
Posts: 52

Kudos [?]: 8 [1], given: 0

### Show Tags

30 Dec 2005, 09:17
1
KUDOS
Guys, The OA is 1,764,000

OE :

The 4 different consonants can be selected in 7C4 ways
The different vowels can be selected in 5C3 ways
The resulting 7 different letters ( 4 consonants & 3 vowels) can be arranged themselves in 7P7 = 7! ways..

So the answer is 7C4 * 5C3 * 7! = 35 *10 * 5040 = 1764000
_________________

"The difference between a smart person and a wise person is that
a smart person knows what to say and
a wise person knows whether or not to say it."

Kudos [?]: 8 [1], given: 0

Director
Joined: 09 Oct 2005
Posts: 712

Kudos [?]: 26 [0], given: 0

### Show Tags

30 Dec 2005, 11:33
Itzrevs wrote:
Guys, The OA is 1,764,000

OE :

The 4 different consonants can be selected in 7C4 ways
The different vowels can be selected in 5C3 ways
The resulting 7 different letters ( 4 consonants & 3 vowels) can be arranged themselves in 7P7 = 7! ways..

So the answer is 7C4 * 5C3 * 7! = 35 *10 * 5040 = 1764000

It seemed so simple at first look)))Good one!10x

Kudos [?]: 26 [0], given: 0

Intern
Joined: 04 Oct 2013
Posts: 4

Kudos [?]: [0], given: 2

Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]

### Show Tags

23 Nov 2013, 05:12
Itzrevs wrote:
From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.

Because each word has to consist of different consonants or vowels, the correct answer is (7*6*5*4)*(5*4*3) and not 7^4*5^3. I used bars to distinguish the numbers representing consonants and vowels to make it more clear.

Kudos [?]: [0], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 43312

Kudos [?]: 139296 [2], given: 12783

Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]

### Show Tags

23 Nov 2013, 05:22
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
Itzrevs wrote:
From 7 consonants and 5 vowels, how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.

OA:
[Reveal] Spoiler:
1,764,000

The # of ways to choose 4 different consonants out of 7 is $$C^4_7=35$$;
The # of ways to choose 3 different vowels out of 5 is $$C^3_5=10$$.

Thus the # of ways to choose 4 different consonants and 3 different vowels is $$35*10=350$$.

Finally these 7 letters can be arranged in 7! ways, therefore the total # of different words is $$350*7!=1,764,000$$.

Hope this helps.
_________________

Kudos [?]: 139296 [2], given: 12783

Intern
Status: preparing for the GMAT
Joined: 16 Jul 2013
Posts: 38

Kudos [?]: 8 [0], given: 5

Concentration: Technology, Entrepreneurship
GMAT Date: 10-15-2013
GPA: 3.53
Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]

### Show Tags

25 Nov 2013, 22:13
I do not think you will see like this question in the test, unless the answer choices contain 350 * 7!.

but this is a good question to practise both concept - combination and permutation- in one question.
_________________

لا الله الا الله, محمد رسول الله

You never fail until you stop trying ,,,

Kudos [?]: 8 [0], given: 5

Current Student
Joined: 01 Oct 2012
Posts: 20

Kudos [?]: 6 [1], given: 0

Location: India
Concentration: Technology, Finance
GMAT 1: 660 Q48 V34
GPA: 3.1
WE: Information Technology (Computer Software)
Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]

### Show Tags

01 May 2014, 08:05
1
KUDOS
Hi,
I still don't get whats wrong with 7P4*5P3?

Kudos [?]: 6 [1], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 43312

Kudos [?]: 139296 [1], given: 12783

Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]

### Show Tags

01 May 2014, 08:53
1
KUDOS
Expert's post
Hi,
I still don't get whats wrong with 7P4*5P3?

That's because we are arranging all 7 letters together.

For example, consider simpler case: how many 4-letter words you can make from 2 consonants {b, c} and two vowels {a, e}. If you arrange them first ({b, c} and {c, b} for consonants and {a, e} and {e, a} for vowels) you'll get 2*2=4 words, which would be wrong. The correct answer is 4!=24.
_________________

Kudos [?]: 139296 [1], given: 12783

Intern
Joined: 18 Oct 2013
Posts: 17

Kudos [?]: 8 [0], given: 13

Location: India
Concentration: General Management, Operations
WE: Engineering (Other)
Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]

### Show Tags

01 May 2014, 21:37
Hello there

Are there ways to come up with sub-types of this particular question?

For example,

A case with 3 distinct vowels & 4 distinct consonants.
A case where the ORDER of the letters DOES NOT matter (OR) a case where ORDER matters.
etc.

OR is there a particular link where such questions are discussed?

Kudos [?]: 8 [0], given: 13

Math Expert
Joined: 02 Sep 2009
Posts: 43312

Kudos [?]: 139296 [0], given: 12783

Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]

### Show Tags

02 May 2014, 01:21
Hello there

Are there ways to come up with sub-types of this particular question?

For example,

A case with 3 distinct vowels & 4 distinct consonants.
A case where the ORDER of the letters DOES NOT matter (OR) a case where ORDER matters.
etc.

OR is there a particular link where such questions are discussed?

The question at hand is where we have distinct letters and the order does matters. If the order does not matter the answer would be $$C^4_7*C^3_5=35*10=350$$.

Theory on Combinations: math-combinatorics-87345.html

DS questions on Combinations: search.php?search_id=tag&tag_id=31
PS questions on Combinations: search.php?search_id=tag&tag_id=52

Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html

Hope this helps.
_________________

Kudos [?]: 139296 [0], given: 12783

Manager
Joined: 19 Mar 2012
Posts: 131

Kudos [?]: 37 [0], given: 368

Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]

### Show Tags

02 May 2014, 08:51
Hi Bunuel
What is wrong with my approach.
Can you please correct me :
Imagine 7 boxes now let's say we are filling first 4 boxes with consonants .First box can be filled with 7 ways.Second with 6 and so on.
Similarly for 3 vowel boxes : first box can be formed with 5 ways , second with 4 ways and third with 3 ways :

So total number of ways =7*6*5*4*5*4*3
And now these letters can be arranged in 7! ways to have different combination.
I know I am wrong.

_________________

Feel Free to Press Kudos if you like the way I think .

Kudos [?]: 37 [0], given: 368

Math Expert
Joined: 02 Sep 2009
Posts: 43312

Kudos [?]: 139296 [0], given: 12783

Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]

### Show Tags

02 May 2014, 09:13
282552 wrote:
Hi Bunuel
What is wrong with my approach.
Can you please correct me :
Imagine 7 boxes now let's say we are filling first 4 boxes with consonants .First box can be filled with 7 ways.Second with 6 and so on.
Similarly for 3 vowel boxes : first box can be formed with 5 ways , second with 4 ways and third with 3 ways :

So total number of ways =7*6*5*4*5*4*3
And now these letters can be arranged in 7! ways to have different combination.
I know I am wrong.

Short answer would be that 7*6*5*4 as well as 5*4*3 will contain repetitions. The number of way to choose 4 letters out of 7 is NOT 7*6*5*4 it's $$C^4_7=\frac{7!}{4!3!}=35$$ and the number of way to choose 3 letters out of 5 is NOT 5*4*3 it's $$C^3_5=\frac{5!}{3!2!}=10$$.
_________________

Kudos [?]: 139296 [0], given: 12783

Non-Human User
Joined: 09 Sep 2013
Posts: 14255

Kudos [?]: 291 [0], given: 0

Re: From 7 consonants and 5 vowels, how many words can be formed [#permalink]

### Show Tags

30 Aug 2017, 11:14
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.
_________________

Kudos [?]: 291 [0], given: 0

Re: From 7 consonants and 5 vowels, how many words can be formed   [#permalink] 30 Aug 2017, 11:14
Display posts from previous: Sort by