number of possible combinations

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lukaswelker: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Wed Mar 26, 2014 6:56 amFollowed by: 1 member

by lukaswelker » Tue Apr 08, 2014 10:29 am

Hey guys, I was lucky to get it right but I really need to understand how

here's the question,

To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse?.

6; 8; 10, 15, 30

Which of the combinations formula should I have used?

Any suggestions?
Cheers
Lukas

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Source: Beat The GMAT — Problem Solving | Tue Apr 08, 2014 10:29 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Apr 08, 2014 10:32 am

To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs and 150 different combinations are possible, how many tables are in the warehouse?

A) 6
B) 8
C) 10
D) 15
E) 30

OA 6

Total # of combinations = (# of ways to select 2 chairs)(# of ways to select 2 tables)
So, 150 = (# of ways to select 2 chairs)(# of ways to select 2 tables)

# of ways to select 2 chairs
5 tables, choose 2 of them.
Since the order of the selected chairs does not matter, we can use combinations.
This can be accomplished in 5C2 ways (10 ways)

Total # of combinations = (# of ways to select 2 chairs)(# of ways to select 2 tables)
150 = (10)(# of ways to select 2 tables)
(# of ways to select 2 tables) = 15

# of ways to select 2 tables
Let N = # of tables.
We have N tables, choose 2.
This can be accomplished in NC2 ways
So, NC2 = 15
Our goal is to find the value of N.

From here, we can just start checking answer choices.
We get 6C2 = 15, so N = 6, which means there are 6 tables.

Answer = A

If anyone is interested, we have a free video on calculating combinations (like 6C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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