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Senior | Next Rank: 100 Posts
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by optimisticsam » Wed Sep 05, 2007 9:11 am
To furnish a room in a model home, a decorator is to select 2 chairs and 2 tables from collection in a warehouse that are all different from each other. If the warehouse contains 5 chairs, and if 150 combinations are possible, how many table are there?

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

I was not sure how to go about this, I just ended up guessing (wrongly).

Any help would be great!

Thanks in advance!
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by samirpandeyit62 » Wed Sep 05, 2007 9:30 am
here we can say

5 chairs can be selected out of 2 in 5C2 ways i.e. 10 ways
this combination for selecting chairs

now acoording to Q

total combinations =150,

i.e. 150 = combination of Chairs X combination of tables (CT)

i.e 150 = 10 X CT

so CT = 15

now CT = (nos of tables) C 2

hence (nos of tables) C 2 = 15

hence nos of tables should be 6 as 6C2 =15

so ans should be "A"
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by optimisticsam » Wed Sep 05, 2007 11:42 am
Is there any quick way to solve xC2=15?

Other than the plugging and chugging the choices thru n!/(k1(n-k)!)?
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