How many combinations of three letters taken from letters

eski wrote:Is this a right GMAT question and of what difficulty?

I'm pretty sure that, in its current form, this would never be a true GMAT question. It's too ambiguous.
The main problem is the assumption that the word "combination" implies that the order of the letters does not matter. If this assumption is correct then Mitch's solution is perfect (as always).

Having said that, I don't think this is necessarily how people interpret the word "combination." For example, when you use a combination lock, the order of the numbers certainly matters.

As you can see in Mitch's solution, we have abc as one combination, but we're not including 5 other arrangements of the 3 letters (acb, bac, bca, cab, cba). Instead, we're just looking at the number of ways to select 3 letters, without considering their order.

To be a true GMAT question, any ambiguity must be removed.

One fix: In how many different ways can 3 letters be selected from {a,a,b,b,c,c,d} if the order in which the letters are selected does not matter. (I'm sure the test-maker could do better than this)

Alternatively, if the order does matter (i.e., abc, acb, bac, bca, cab and cba are considered different), then the wording could be: How many different 3-letter words can be constructed if the 3 letters are selected from {a,a,b,b,c,c,d}?

Cheers,
Brent