A word consists of 10 letters; 6 consonants and 4vowels. Three letters

Question

A word consists of 10 letters; 6 consonants and 4vowels. Three letters are chosen at random. What is the probability that more than one vowel will be selected ?

A. 1/7

B. 1/3

C. 17/42

D. 4/5

E. 6/7

GMATCoachBen · Accepted Answer

For probability, we need to find:  \frac{ # of Desired Combinations }{ # of Total Combinations}

We use the combinations formula, because order doesn't matter here: nCr =  \frac{n!}{r!(n−r)!} . (nCr means "n choose r" — the # of combinations when out of "n" items we choose "r" items)

For the Desired Combinations, there are two ways to get "more than one vowel"; we can have either: 
A) 2 vowels AND 1 consonant OR 
B) 3 vowels AND 0 consonants

Note that "OR" means we "add", and "AND" means we multiply.

Step 1: 
Combinations with 2 vowels AND 1 consonant (we are choosing 2 vowels out of 4, and 1 consonant out of 6) = 4C2 * 6C1 =  \frac{4*3}{2}  * 6 =  36

Step 2: 
Combinations with 3 vowels (AND 0 consonants) = 4C3 =  4  (Note: there is always only 1 combination when we choose 0 items, so we don't need to do a calculation for the 0 consonants)

Step 3: 
Total Combinations, choosing 3 letters out of 10 letters = 10C3 =  \frac{10*9*8}{(3*2)}  =  120

Step 4: 
Probability =  \frac{Combinations With 2 or 3 vowels }{ Total Combinations}  =  \frac{36 + 4 }{ 120}  =   1/3

MBAHOUSE · Answer

Instead to attack directly what he asks, I calculated what he doesn’t ask and subtracted from the sample set that is always 1. It’s faster.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

A word consists of 10 letters; 6 consonants and 4vowels. Three letters

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A word consists of 10 letters; 6 consonants and 4vowels. Three letters

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards