In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2

[BTGmoderatorDC]

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

[Scott@TargetTestPrep]

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

Solution:

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