4th Edition of MGMAT's Word Translations Guide

I'm confused on why using the same combinations method works for one problem but not the other, though they are seemingly identical types of problems. They both work out for me when I follow the domino effect, but for extra practice I was trying to work through them with counting/combinatorics and got stuck.

1) Chapter 5, pg 93, problem 9:
"In a bag of marbles, there are 3 red, 2 white, and 5 blue. If Bob takes 2 marbles out of the bag, what is the probability that he will have one white and one blue marble?"

So in this case we have 10!/(2!8!) = 45 different combinations of marbles. Then the MGMAT book states that since there are 2 white marbles and 5 blue marbles, so there are 2 x 5 = 10 different white-blue combinations. Therefor, the probability of selecting a blue and white combination is 10/45 or 2/9. This is great, it agrees with the picking scenarios solution.

2) Chapter 12, pg 190, sample question:
"A miniature gumball machine contains 7 blue, 5 green, and 4 red gumballs, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?"

This question has an official answer of 1/4, using the domino effect.. great.. makes sense; however, when trying with combinatorics, following the same idea as question 1, I get: 16!/(3!13!) = 160 different combinations of marbles. Since there are 7 blue, 5 white, and 4 red marbles, there are 7 x 5 x 4= 140 different white-blue-red combinations. Therefor, the probability of selecting a red, blue, and white combination is 140/160 or 7/8. Not quite the same.

Any ideas on what I'm doing wrong?

I get: 16!/(3!13!) = 160 different combinations of marbles. Since there are 7 blue, 5 white, and 4 red marbles, there are 7 x 5 x 4= 140 different white-blue-red combinations. [/quote]

Hi llindah,
Please rework your math here. When I calculate 16!/(3!13!) I get (16 * 15 * 14)/6, which can be simplified to 8 * 5 * 14 or 560. I hope that helps!

Thank you,

_________________
Jamie Nelson
ManhattanGMAT Instructor

doH! Stupid mistakes will be the end of me, and I even checked my work~

That explains a lot, thanks!

:)

_________________
Tim Sanders
Manhattan GMAT Instructor