Permutation and Combination -Letter Arrangements

s91arvindh wrote: List A: C, M, G, L, S, U, O
List B: X, Y, Z, P, T

How many different 4-letter arrangements can be made by selecting 2 letters each from list A and list B above?
a) 4500 b) 3060 c) 2930 d) 5040

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Take the task of selecting and arranging the letters, and break it into stages.

Stage 1: Select 2 letters from list A.
Since the order in which we SELECT the two letters does not matter, we can use combinations.
We can select 2 letters from 7 letters in 7C2 ways (21 ways)

Aside: If anyone is interested, we have a free video on calculating combinations (like 7C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

Stage 2: Select 2 letters from list B.
We can select 2 letters from 5 letters in 5C2 ways (10 ways)

Now that we've selected the 4 letters we'll use to create our word, it's just a matter of arranging them.

Stage 3: Arrange the 4 letters.
We have a nice rule for this. We can arrange n unique objects in a row in n! ways.
So, we can complete stage 3 in 4! (24 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a 4-letter word) in (21)(10)(24) ways ([spoiler]= 5040 ways[/spoiler])

Answer: D

Cheers,
Brent

Aside: For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775