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

 It is currently 18 Oct 2019, 07:42

### 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

# In how many ways all the letters of the word WEAPONS can be arranged

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

05 Mar 2019, 21:42
00:00

Difficulty:

95% (hard)

Question Stats:

21% (02:24) correct 79% (01:24) wrong based on 38 sessions

### HideShow timer Statistics

In how many ways all the letters of the word WEAPONS can be arranged such that in any of the arrangements, no two vowels will be together?

A. $$^5C_3 * 3!$$

B. $$3! * 4!$$

C. $$^5C_3 * 4!$$

D. $$7! – 5! * 3!$$

E. $$^5C_3 * 3! * 4!$$

_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5018
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

Updated on: 08 Mar 2019, 03:16
WEAPONS = 7! ways total arrangement
vowels = EAO 3! ways and consonants WPNS = 4! ways

these vowels can be arranged in 5c3 ways between 4 WPNS

5c3*3!*4!
IMO E

EgmatQuantExpert wrote:
In how many ways all the letters of the word WEAPONS can be arranged such that in any of the arrangements, no two vowels will be together?

A. $$^5C_3 * 3!$$

B. $$3! * 4!$$

C. $$^5C_3 * 4!$$

D. $$7! – 5! * 3!$$

E. $$^5C_3 * 3! * 4!$$

Originally posted by Archit3110 on 06 Mar 2019, 01:57.
Last edited by Archit3110 on 08 Mar 2019, 03:16, edited 1 time in total.
Intern
Joined: 23 Oct 2013
Posts: 44
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

06 Mar 2019, 19:23
is ans E

arrange consonants as _W_P_N_S_ consonants E,A,O can be placed in any 5 blanks so 5c3

consonants can be arranged within itself in 3!
vowels can be arranged in 4! ways

so 5c3*4!*3!
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

07 Mar 2019, 22:42

Solution

Given:
In this question, we are given
• A specific word is given: WEAPONS, of which all the letters can be arranged to form different words

To find:
We need to determine
• How many such arrangements are possible, where no two vowels will be together

Approach and Working:
In the given word “WEAPONS”, there are 4 consonants: W, P, N, S and 3 vowels: E, A, O.
• When we say that no two vowels are together, it means there will be at least one consonant between any two vowels.

As there are 4 consonants, let us first put them, as shown in the following figure:

Now, for the 3 vowels, there will be actually 5 places where any of those vowels can be placed.

• Out of the 5 possible places, 3 will be chosen for the vowels in $$^5C_3$$ ways.
• Also, the vowels can rearrange themselves in 3! ways and the consonants can rearrange themselves in 4! ways.
• Therefore, the total number of possible arrangements = $$^5C_3 * 3! * 4!$$

Hence, the correct answer is option E.

_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

07 Mar 2019, 22:45
Archit3110 wrote:
WEAPONS = 7! ways total arrangement
vowels = EAO WPNS = 5! ways and total vowels = 3 ;3! ways

7!-5!*3!
IMO D

Hey Archit3110,
In your calculation, you missed those cases where two vowels can be together. You only removed the cases where all 3 vowels are together.
_________________
Senior Manager
Status: Manager
Joined: 02 Nov 2018
Posts: 280
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

07 Mar 2019, 23:57
1
There are 7 letters in the word WEAPONS with 3 vowels and 4 consonant of the 5 possible places, 3 will be chosen for the vowels in 5C35C3 ways.the vowels can rearrange themselves in 3! ways and the consonants can rearrange themselves in 4! ways.. Hence, number of arrangements of letters such that all vowels are all together is 5C3∗3!∗4! so the correct answer is E
_________________
Give a kudos if u find my post helpful. kudos motivates active discussions

Intern
Joined: 13 Jul 2018
Posts: 7
GMAT 1: 650 Q47 V33
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

08 Mar 2019, 01:55
1
EgmatQuantExpert wrote:
Archit3110 wrote:
WEAPONS = 7! ways total arrangement
vowels = EAO WPNS = 5! ways and total vowels = 3 ;3! ways

7!-5!*3!
IMO D

Hey,
In your calculation, you missed those cases where two vowels can be together. You only removed the cases where all 3 vowels are together.

And what is the best way to do it with that approach? (removing csaes from the total)
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5018
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

08 Mar 2019, 03:13
EgmatQuantExpert wrote:
Archit3110 wrote:
WEAPONS = 7! ways total arrangement
vowels = EAO WPNS = 5! ways and total vowels = 3 ;3! ways

7!-5!*3!
IMO D

Hey Archit3110,
In your calculation, you missed those cases where two vowels can be together. You only removed the cases where all 3 vowels are together.

EgmatQuantExpert
Intern
Joined: 21 Sep 2016
Posts: 5
Location: Saudi Arabia
Concentration: Finance, Entrepreneurship
WE: Corporate Finance (Consumer Electronics)
In how many ways all the letters of the word WEAPONS can be arranged  [#permalink]

### Show Tags

09 Mar 2019, 08:30
When we insert 1 vowel in the middle of each consonant and 1 vowel each at the corner, in total, it would make 9 spaces, however WEAPONS has only 7 spaces.
In how many ways all the letters of the word WEAPONS can be arranged   [#permalink] 09 Mar 2019, 08:30
Display posts from previous: Sort by