In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning.
Option:
A) 36
B) 144
C) 288
D) 864
E) 1728
OA D
Source: e-GMAT
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2
This topic has expert replies
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Solution:BTGmoderatorDC wrote: ↑Thu Apr 08, 2021 1:29 amIn how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning.
Option:
A) 36
B) 144
C) 288
D) 864
E) 1728
OA D
There are 4C2 = 6 ways to choose 2 vowels from 4 vowels, and similarly, there are 4C2 = 6 ways to choose 2 consonants from 4 consonants Therefore, there are 6 x 6 = 36 different words with a particular set of 2 vowels and 2 consonants.
However, for each of these 36 words, since the 4 letters can be arranged in any order, there are a total of 4! x 36 = 24 x 36 = 864 words possible.
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
