This one is easy enough to do by hand:
ABACUS has 3 vowels and 3 consonants. You want all the vowels together, so the possibilities are:
V V V C C C
C V V V C C
C C V V V C
C C C V V V
Now in the case of the vowels, there are only 3 unique arrangements, because there's a repeated letter:
AAU
AUA
UAA
(By the way, as a side note, there are usually n! unique arrangements of n elements, but when you have a repeated element, you have to divide by the factorial of the number of repeats. For example, this would be 3! unique arrangements, but because the A appears twice, it's actually 3! / 2! = 3. And if, for example, you had 7 elements, and 2 of them repeated twice, then it would bt 7! / (2! * 2!) )
In the case of the consonants, there are no repeats, so there are 3! = 6 unique arrangements. So:
V V V C C C (3 arrangements for the vowels) * (6 arrangements for the consonants) = 18 total arrangements
C V V V C C same thing, 3*6 = 18
C C V V V C Again, 18.
C C C V V V Again, 18.
Total arrangements: 72
Make sense?
Last edited by
Rich@VeritasPrep on Wed Jun 16, 2010 6:20 am, edited 2 times in total.
Rich Zwelling
GMAT Instructor, Veritas Prep
