papgust wrote:NikolayZ,
I took this problem from Arun sharma's Quantitative aptitude for CAT. I believe that the answer choices must be correct.
I've never heard of the source, but here are two problems with the question:
1) there are only 4 answer choices, so it's clearly not designed for the GMAT; and
2) it's unanswerable without further information. In particular, we need to know if the letters in each category are distinct.
For example, if the 3 capital consonants were A, A and A, we'd only have 1 choice for our first letter. If the 3 capital consonants were A, B and C, we'd have 3 such choices.
If we assume that all the letters in each category are distinct (something we'd never have to do on a more realistic question):
Part 1: 3 choices for the first letter.
Part 2: first, let's select our potential letters.
Consonants - choosing 3 out of 5 = 5C3 = 5!/3!2! = 5*4/2 = 10
Vowels - choosing 2 out of 4 = 4C2 = 4!/2!2! = 4*3/2 = 6
So, we have 10*6 = 60 possible selections of letters.
Second, let's see in how many different ways we can arrange those 5 letters. Simple enough, there are n! different ways to arrange n distinct objects, so 5!.
Therefore, our final answer is:
3*60*5! = 180 * 120 = 21600
However, as I said above, this is a very poorly written question and, as a result, I'd be suspicious of anything from that source.
