Hi All,
To start, this question is really poorly-worded, but the math behind it is just "Permutation math." There are a number of different ways to approach it - and even if you don't know how to do all of the math "all at once", you can still solve it by breaking the calculation down into pieces.
We're asked for the number of 4-letter words that can be formed using the letters in the word ENGLISH, with the following restrictions:
1) The letters G and L must be in the word,
2) The G must appear before the L (this is meant to mean that the G appears IMMEDIATELY BEFORE the L, although the way the prompt is written is vague on this point).
3) Letter repetition is NOT allowed.
Since we MUST use the G and the L, we're going to choose 2 additional letters from the 5 remaining letters (E, N, I, S and H). Since the G must come 'immediately before' the L, we can 'map out' the various ways that that can happen:
1st option: G L _ _
Here, the first blank would be filled by one of the 5 other letters (and once we choose a letter, the second blank would be filled with one of the 4 remaining letters). Thus, there are (5)(4) = 20 words that begin with "GL"
From here, we just have to account for all of the ways that the L can immediately follow the G:
G L _ _
_ G L _
_ _ G L
Each of these 3 possibilities would have 20 options each... (3)(20) = 60 possible words
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
