S99-14

good ques.... tricked me into selecting 12. I didnt notice that repetition is allowed. Silly mistake.

I'm wondering why the initial selection of the consonants and vowels didn't factor into the calculation. I agree that such a high number isn't in any of the options.

The initial 3 consonants and 2 vowels can be any of the 21 and 5 consonants and vowels resp. in the english alphabet? I think the only thing that makes this wrong is the assumption that the Vowels and Consonants in Simplastic is taken from English, and it doesn't say that anywhere.

I got 21C3 X 5C2 X 108

The Simplastic language has only 2 unique values and 3 unique consonants. Every noun in Simplastic has the structure CVCVC, where C stands for a consonant and V stands for a vowel. How many different nouns are possible in Simplastic?

A. 9
B. 12
C. 36
D. 72
E. 108

Official Solution:

The Simplastic language has only 2 unique values and 3 unique consonants. Every noun in Simplastic has the structure CVCVC, where C stands for a consonant and V stands for a vowel. How many different nouns are possible in Simplastic?

A. 9
B. 12
C. 36
D. 72
E. 108


This Combinatorics problem asks you to compute the number of possible nouns in Simplastic, given the template CVCVC.

We have a series of successive choices:

• Pick the first consonant
• Pick the first vowel
• Pick the second consonant
• Pick the second vowel
• Pick the third consonant

So we need to count the choices we have at each stage, and then multiply these choices together. We have 3 choices for each consonant and 2 choices for each vowel. Note that we can reuse consonants and vowels. For instance, imagine that the consonants are {g, l, t} and the vowels are {a, u}. Here are some valid nouns in Simplastic:

gagag

gulat

lugul

Thus, we write \(3 \times 2 \times 3 \times 2 \times 3 = 108\).


Answer: E

Hi Bunuel,

I wanted to clarify the combinatorics method that you used, so when it is CVCVC and 3 possibilities for C and 2 for V, did you do 3C1x2C1x3C1x2C1x3C1 = 108?

Thanks!