BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

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

by Vincen » Thu Sep 03, 2020 5:41 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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. \(^5C_3\cdot 3!\)

B. \(3!\cdot 4!\)

C. \(^5C_3\cdot 4!\)

D. \(7!-5!\cdot 3!\)

E. \(^5C_3\cdot 3!\cdot 4!\)

Answer: E

Source: e-GMAT
Top
Source: — Problem Solving |
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

Re: In how many ways all the letters of the word WEAPONS can be arranged such that in any of the arrangements, no two vo

by deloitte247 » Mon Sep 07, 2020 7:44 am
Arranging all the letters of the word WEAPONS such that no two vowels will be together


There are 7 letters in the word WEAPONS with 3 vowels -> E, A, and O
All possible arrangement of WEAPONS = 8!
There are 4 consonants present -> WPNS


The vowels can be arranged among themselves in 3! ways
The consonants can also be arranged among themselves in 4! ways
_W_P_N_S_


There are 5 possible positions for the 3 vowels to occupy beside the consonants such that no two vowels will be together, and this means they can be arranged in 5C3*3!*4!

=>5C3*3!*4!
Answer = E
Top
Legendary Member
Posts: 2499
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

Re: In how many ways all the letters of the word WEAPONS can be arranged such that in any of the arrangements, no two vo

by swerve » Mon Sep 07, 2020 12:52 pm
Vincen wrote: ↑
Thu Sep 03, 2020 5:41 am
 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. \(^5C_3\cdot 3!\)

B. \(3!\cdot 4!\)

C. \(^5C_3\cdot 4!\)

D. \(7!-5!\cdot 3!\)

E. \(^5C_3\cdot 3!\cdot 4!\)

Answer: E

Source: e-GMAT
There are \(7\) letters in the word WEAPONS with \(3\) vowels and \(4\) consonants 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 \(5C3\cdot 3! \cdot 4!\), so the correct answer is E
Top
Post new topic Post Reply
• Page 1 of 1