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!
GMAT Prep Combinations
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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"
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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Is there any quick way to solve xC2=15?
Other than the plugging and chugging the choices thru n!/(k1(n-k)!)?
Other than the plugging and chugging the choices thru n!/(k1(n-k)!)?