It is currently 20 Nov 2017, 14:43

### 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

# How many words of 2 distinct vowels and 3 distinct consonant

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 30 May 2005
Posts: 274

Kudos [?]: 44 [1], given: 0

How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

### Show Tags

02 Sep 2005, 17:24
1
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:12) correct 0% (00:00) wrong based on 49 sessions

### HideShow timer Statistics

How many words of 2 distinct vowels and 3 distinct consonants can be made using the English Alphabet?

[Reveal] Spoiler:
my approach was

C 5 2 * C 21 3 / C 26 5

PLz correct me I am wrong

Last edited by Bunuel on 20 Oct 2013, 22:57, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 44 [1], given: 0

Senior Manager
Joined: 29 Nov 2004
Posts: 477

Kudos [?]: 37 [1], given: 0

Location: Chicago
Re: ps TRICKY Combination PROBLEMS [#permalink]

### Show Tags

02 Sep 2005, 17:46
1
KUDOS
I am not sure why you are dividing with 26C5, there is no probability involved

IMO the best way is (21C3*5C2)*5!

because if we rearrange each 5 letter words we get 5! different words...
_________________

Fear Mediocrity, Respect Ignorance

Kudos [?]: 37 [1], given: 0

Intern
Joined: 19 Sep 2013
Posts: 21

Kudos [?]: 16 [2], given: 17

GMAT 1: 720 Q49 V38
GPA: 3.8
Re: ps TRICKY Combination PROBLEMS [#permalink]

### Show Tags

20 Oct 2013, 22:35
2
KUDOS
If you still need further clarification, it goes like this...

from 5 vowels you need to pick 2 and 21 consonants you need to pick 3

5C2* 21C3 . These 5 letters can be arranged in 5! as they are all distinct , ergo 5C2*21C3*5!
_________________

Kudos if you like my post

Kudos [?]: 16 [2], given: 17

Intern
Joined: 19 Sep 2013
Posts: 21

Kudos [?]: 16 [0], given: 17

GMAT 1: 720 Q49 V38
GPA: 3.8
Re: ps TRICKY Combination PROBLEMS [#permalink]

### Show Tags

20 Oct 2013, 22:36
If you still need further clarification, it goes like this...

from 5 vowels you need to pick 2 and 21 consonants you need to pick 3

5C2* 21C3 . These 5 letters can be arranged in 5! as they are all distinct , ergo 5C2*21C3*5!
_________________

Kudos if you like my post

Kudos [?]: 16 [0], given: 17

Current Student
Joined: 06 Sep 2013
Posts: 1972

Kudos [?]: 742 [0], given: 355

Concentration: Finance
Re: How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

### Show Tags

30 Dec 2013, 05:41
mandy wrote:
How many words of 2 distinct vowels and 3 distinct consonants can be made using the English Alphabet?

[Reveal] Spoiler:
my approach was

C 5 2 * C 21 3 / C 26 5

PLz correct me I am wrong

I got the following

We have a 5 letter word

We need to pick 3 out of 21 consonants and 2 out of 5 vowels

So we have slot method _ _ _ _ _

So it boils down to 5C3 (21*20*19) (5*4*3)

5 ways of arranging the 3 consonants and two vowels * We have 21 options for the first consonant, 20 for the second, 19 for the third since they have to be different and same for vowels

Is this approach correct?

Let me know will you?

Thanks

Cheers!
J

Kudos [?]: 742 [0], given: 355

Non-Human User
Joined: 09 Sep 2013
Posts: 15613

Kudos [?]: 283 [0], given: 0

Re: How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

### Show Tags

02 Jul 2016, 10:33
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 [?]: 283 [0], given: 0

Manager
Joined: 02 Jul 2016
Posts: 81

Kudos [?]: 3 [0], given: 7

Re: How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

### Show Tags

27 Jul 2016, 23:55
please let me know if my approach is wrong
I have solved the question by Fundamental Principle of Counting
vowels{a,e,i,o,u}=5
consonants 26-5=21
In the 5 letter word
2 vowels need to be there along with 3 consonants
for filling vowels
5x4=20 ways/words
for filiing consonants
21x20x19 ways/words
hence the number of ways/words for forming a 5 letter word according to the given conditions will be
20X21X20X19 ways/words

Kudos [?]: 3 [0], given: 7

Senior Manager
Joined: 23 Apr 2015
Posts: 332

Kudos [?]: 116 [0], given: 36

Location: United States
WE: Engineering (Consulting)
Re: How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

### Show Tags

24 Aug 2016, 11:25
suramya26 wrote:
please let me know if my approach is wrong
I have solved the question by Fundamental Principle of Counting
vowels{a,e,i,o,u}=5
consonants 26-5=21
In the 5 letter word
2 vowels need to be there along with 3 consonants
for filling vowels
5x4=20 ways/words
for filiing consonants
21x20x19 ways/words
hence the number of ways/words for forming a 5 letter word according to the given conditions will be
20X21X20X19 ways/words

Hi Suramya26,

There are 2 sets here one with 5 vowels {a,e,i,o,u} and other with 21 consonants.
The word formed should have 5 letters in which 2 are vowels and 3 are consonants.

from {a,e,i,o,u} to pick only 2 , there are $$5C2$$ ways.
from 21 consonants to pick 3, there are $$21C3$$ ways.
But the 5 letter word can rearranged in to $$5!$$ ways, (AEBCD is different from ABCDE)

so answer is $$5C2 * 21C3 * 5!$$.

Kudos [?]: 116 [0], given: 36

Senior Manager
Joined: 17 Jun 2015
Posts: 261

Kudos [?]: 40 [0], given: 165

GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
Re: How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

### Show Tags

07 Sep 2016, 17:16
So, we are given 2 distinct vowels and 3 distinct consonants is just to confuse and bring in the identical concept. It might just be a question of forming number of words using 5 different alphabets. 5!

But, if we are also select the 2 distinct vowels and 3 distinct consonants, the selection for vowels would be 5C2 and consonants would be 21C3. And then these would have to be arranged i.e. 5C2 * 21C3 * 5!?

Bunuel pls help
_________________

Fais de ta vie un rêve et d'un rêve une réalité

Kudos [?]: 40 [0], given: 165

Director
Joined: 05 Mar 2015
Posts: 963

Kudos [?]: 291 [0], given: 41

Re: How many words of 2 distinct vowels and 3 distinct consonant [#permalink]

### Show Tags

12 Jul 2017, 19:10
hdwnkr wrote:
So, we are given 2 distinct vowels and 3 distinct consonants is just to confuse and bring in the identical concept. It might just be a question of forming number of words using 5 different alphabets. 5!

But, if we are also select the 2 distinct vowels and 3 distinct consonants, the selection for vowels would be 5C2 and consonants would be 21C3. And then these would have to be arranged i.e. 5C2 * 21C3 * 5!?

Bunuel pls help

We have not been provided any marked vowels/consonants
rather we need to select any from all those
Also we can form any words either having any meaning or meaningless

thus on first step we have to select ,than on second step arrange them..

so your later consideration must be correct one..

Kudos [?]: 291 [0], given: 41

Re: How many words of 2 distinct vowels and 3 distinct consonant   [#permalink] 12 Jul 2017, 19:10
Display posts from previous: Sort by