BTGModeratorVI wrote: ↑Mon Jul 13, 2020 7:42 am
In how many ways can the letters of word "EDUCATION" be arranged such that all the vowels always appear together?
A) 9!
B) 5!*4!
C) 5!*5!
D) 5!*4!*2!
E) 6!*4!
Answer:
C
Source: Math Revolution
VOWELS: E, U, A, I, O
CONSONANTS: D, C, T, N
Take the task of arranging the letters and
break it into stages.
Stage 1: Arrange the 5 vowels
We can arrange n unique objects in n! ways
So, we can arrange the 5 vowels in 5! ways
In other words, we can complete stage 1 in
5! ways
Stage 2: Arrange the 4 consonants
There are 4 unique objects to arrange.
We can complete stage 2 in
4! ways
Stage 3: The two groups of letters (the vowel group and the consonant group)
There are two options:
1) CONSONANTS-VOWELS
1) VOWELS-CONSONANTS
We can complete stage 3 in
2 ways
By the Fundamental Counting Principle (FCP), we can complete the 3 stages (and thus arrange all 9 letters) in
(5!)(4!)(2) ways.
Answer: D
Cheers,
Brent
