Problem Solving

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

a. 6
b. 8
c. 10
d. 15
e. 30

No. of ways of selecting 2 chairs from 5 chairs = 5C2
Let us assume that no. of tables in the warehouse = n
Then no. of ways of selecting 2 tables from n tables = nC2

Then 5C2 * nC2 = 150
5!/{(2!) * (5 - 2)!} * n!/{(2!) * (n - 2)!} = 150
(5 * 4 * 3!)/(2! * 3!) * n!/{(2!) * (n - 2)!} = 150
(5 * 4)/(2) * n!/{(2!) * (n - 2)!} = 150
10 * n!/{(2!) * (n - 2)!} = 150
n!/(n - 2)! = 15 * 2
(n * (n - 1) * (n - 2)!/(n - 2)! = 30
n(n - 1) = 30
n² - n - 30 = 0
(n - 6)(n + 5) = 0
n = 6, -5(not possible)
So, [spoiler]n = 6[/spoiler]

The correct answer is A.

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

a. 6
b. 8
c. 10
d. 15
e. 30

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

# of ways to select 2 chairs
5 tables, choose 2 of them.
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

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

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

Cheers,
Brent