probablity dessert platters

[poonamchiK]

In a resturant's dessert paltter, there are 6 different kinds of cheese and 2 different kinds of fruits. If each platter consists of equal no. of cheese and fruits, how many different platters can be made?
a. 8
b. 12
c. 15
d. 21
e 27

correct ans : e

[accounts]

We need equal number of cheese and fruits to make a platter. This can be done when

(1 type of cheese and 1 type of fruit) OR (2 type of cheese and 2 type of fruits)

Note: as types of fruits are 2 and types of cheese 6 ... fruits become the deciding factor.

( 6C1 X 2C1) OR ( 6C2 x 2C2 )
(6*2) + (15 x1 )
= 27 => E

[RonPurewal]

We need equal number of cheese and fruits to make a platter. This can be done when

(1 type of cheese and 1 type of fruit) OR (2 type of cheese and 2 type of fruits)

Note: as types of fruits are 2 and types of cheese 6 ... fruits become the deciding factor.

( 6C1 X 2C1) OR ( 6C2 x 2C2 )
(6*2) + (15 x1 )
= 27 => E

this works.

as an alternative, note that you should easily be able to LIST the possibilities in the time given, and then COUNT the items in your list. (to facilitate this, it's best to call the cheeses 1, 2, 3, 4, 5, 6 and the fruits 1 and 2.)

try making this list; make sure that you can do so in well under the two-minute guideline.