The sequential removal of marbles is a total red herring and you can ignore it. (This happens sometimes in combinatorics problems! To spot cases like this, think about whether what the problem is telling you is actually different from the simpler case. Is removing three marbles then four marbles (without looking at them) different from removing 7 marbles? Nope - that's like saying that eating four cookies then three cookies right afterwards, is somehow different from eating seven cookies all in a row.)
Now let's build up the probability.
probability = good cases / total cases
A 'good' case is one where the three marbles remaining are all the same color. They can't all be alabaster, since there definitely aren't enough alabaster marbles. They could all be cerulean; since there are exactly three cerulean marbles, there's only
one way for that to happen. They could also all be magenta. Suppose that the magenta marbles were labeled A, B, C, D, and E. How many possible cases are there where three magenta marbles are left over?
ABC
ABD
ABE
ACD
ACE
ADE
BCD
BCE
BDE
CDE
That's ten possibilities. So, there are eleven possible cases where the three marbles left over are all the same color.
I stopped at this point and picked the one answer choice that has 11 in the numerator.That's what you should do on the GMAT! But if you're just curious about the math, here's where the 120 in the denominator comes from. How many total cases are there? That is, how many ways can 3 marbles be left over, whether they're all the same or not? That's '10 choose 3', or 10!/(7!*3!), which equals 120.
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