lheiannie07 wrote:In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?
A. None of these
B. 64
C. 120
D. 36
E. 360
Vowels: E, A, I
Consonants: D, T, L
Spaces:
#1,
#2,
#3,
#4,
#5,
#6,
Take the task of arranging the letters and break it into
stages.
Stage 1: Select a vowel to go in space #1
There are 3 vowels to choose from, so we can complete stage 1 in
3 ways
Stage 2: Select a vowel to go in space #3
There are 2 remaining vowels from which to choose, so we can complete this stage in
2 ways.
Stage 3: Select a vowel to go in space #5
There is 1 remaining vowel from which to choose, so we can complete this stage in
1 ways.
Stage 4: Select a consonant to go in space #2
There are 3 consonants to choose from, so we can complete stage 4 in
3 ways .
Stage 5: Select a consonant to go in space #4
There are 2 remaining consonants from which to choose, so we can complete this stage in
2 ways.
Stage 6: Select a consonant to go in space #6
There is 1 remaining consonant from which to choose, so we can complete this stage in
1 ways.
By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus arrange all of the letters) in
(3)(2)(1)(3)(2)(1) ways ([spoiler]= 36 ways[/spoiler])
Answer:
D
--------------------------
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video:
https://www.gmatprepnow.com/module/gmat- ... /video/775
You can also watch a demonstration of the FCP in action:
https://www.gmatprepnow.com/module/gmat ... /video/776
Then you can try solving the following questions:
EASY
-
https://www.beatthegmat.com/what-should- ... 67256.html
-
https://www.beatthegmat.com/counting-pro ... 44302.html
-
https://www.beatthegmat.com/picking-a-5- ... 73110.html
-
https://www.beatthegmat.com/permutation- ... 57412.html
-
https://www.beatthegmat.com/simple-one-t270061.html
MEDIUM
-
https://www.beatthegmat.com/combinatoric ... 73194.html
-
https://www.beatthegmat.com/arabian-hors ... 50703.html
-
https://www.beatthegmat.com/sub-sets-pro ... 73337.html
-
https://www.beatthegmat.com/combinatoric ... 73180.html
-
https://www.beatthegmat.com/digits-numbers-t270127.html
-
https://www.beatthegmat.com/doubt-on-sep ... 71047.html
-
https://www.beatthegmat.com/combinatoric ... 67079.html
DIFFICULT
-
https://www.beatthegmat.com/wonderful-p- ... 71001.html
-
https://www.beatthegmat.com/permutation- ... 73915.html
-
https://www.beatthegmat.com/permutation-t122873.html
-
https://www.beatthegmat.com/no-two-ladie ... 75661.html
-
https://www.beatthegmat.com/combinations-t123249.html
Cheers,
Brent
