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
Answer is D
Derivation :
Selection of 2 letters from list A 7*6 ways
Selection of 2 letters from list B 5*4 ways
Total ways will be (7*6)*(5*4)
Stuck here
Permutation and Combination -Letter Arrangements
This topic has expert replies
-
- Junior | Next Rank: 30 Posts
- Posts: 22
- Joined: Sat Apr 19, 2014 5:24 am
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.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
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
Last edited by Brent@GMATPrepNow on Fri May 02, 2014 6:35 am, edited 1 time in total.
-
- Junior | Next Rank: 30 Posts
- Posts: 22
- Joined: Sat Apr 19, 2014 5:24 am