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# A certain candy store sells jellybeans in the following six flavors on

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
A certain candy store sells jellybeans in the following six flavors on  [#permalink]

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01 Aug 2018, 21:43
10
00:00

Difficulty:

95% (hard)

Question Stats:

37% (02:43) correct 63% (02:44) wrong based on 76 sessions

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A certain candy store sells jellybeans in the following six flavors only: banana, chocolate, grape, lemon, peach and strawberry. The jellybeans are sorted into boxes containing exactly 2, 3 or 4 different flavors, with each possible assortment of flavors appearing in exactly one box. What is the probability that any given box contains grape jellybeans?

A. $$\frac{1}{6}$$

B. $$\frac{1}{3}$$

C. $$\frac{2}{5}$$

D. $$\frac{1}{2}$$

E. $$\frac{3}{4}$$

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Joined: 30 May 2018
Posts: 44
Location: India
GMAT 1: 680 Q49 V33
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WE: Engineering (Energy and Utilities)
A certain candy store sells jellybeans in the following six flavors on  [#permalink]

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02 Aug 2018, 00:08
2
To find out the outcomes with g, we have to subtract from the all outcomes the ways in which g is NOT included.

So it'd be:
6C2 - 5C2 = 5
6C3 - 5C3 = 10
6C4 - 5C4 = 10
25 ways in which g is contained.

Total 50 ways, so 25/50 = 1/2.

D

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A certain candy store sells jellybeans in the following six flavors on  [#permalink]

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21 Dec 2018, 07:10
1
There are 3 options - We can make a combination of 3 different packs - with 2,3 or 4 flavors .

1st option - pack of 2 different flavors ( _ _ )
Total number of ways the flavor can be picked is 6C2.
Now we assume that between the two places, we have already picked the grape flavor. Then we can pick one more flavor and the number of ways to do that is 5C1.

2nd option - pack of 3 flavors ( _ _ _ )
Total number of ways the flavor can be picked is 6C3.
Now we assume that between the three places, we have already picked the grape flavor. Then we can pick two more flavor and the number of ways to do that is 5C2.

3rd option - pack of 4 flavors ( _ _ _ _ )
Total number of ways the flavor can be picked is 6C4.
Now we assume that between the four places, we have already picked the grape flavor. Then we can pick three more flavor and the number of ways to do that is 5C3.

Therefore, probability of picking a box with Grape flavor is

(5C1 + 5C2 + 5C3)/(6C2 + 6C3 + 6C4) = 25/50 = 1/2.

A certain candy store sells jellybeans in the following six flavors on   [#permalink] 21 Dec 2018, 07:10
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