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Flavors = L, C, V, S (4)
Shape = S, H, C (3)
Size = S, L (2)

Nina wants = Large, Star, lemon

At least 2 of three = Any 2 + All 3
=> (Large, Star) + (Star+Lemon) + (Large+Lemon) + (Large+Lemon+Star)
=> 4 + 2 + 3 + 1 - 3 = 10 - 3 = 7
Subtracting the duplicates for the choice (Large+Lemon+Star)

Total possibilities = 4*3*2 = 24
Probability = 7/24

Option C

Bunuel
A bakery sells cookies in four flavors: lemon, chocolate, vanilla, and strawberry. Cookies are made in three shapes: star, heart, and circle. Cookies also come in two sizes: small and large. The bakery has an equal number of cookies of each possible flavor-shape-size combination. Nina wants a large, star-shaped, lemon cookie. If her friend randomly picks one cookie from the display, what is the probability that the cookie picked has at least two of the three features Nina wants?

A. 1/24
B. 1/4
C. 7/24
D. 3/8
E. 17/24

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We know that,
Flavors : 4 (Lemon, chocolate, vanilla, strawberry)
Shapes : 3 (star, heart,circle)
Sizes : 2 (small, large)

Total combinations = 4*3*2 = 24

Nina wants a large star shaped lemon cookie. We want to know probability that the cookie picked has atleast 2 of the 3 features Nina wants

Count of cookie with all 3 features = 1
Count of cookie with exactly 2 features = (Lemon+Star+not Large) + (Lemon+ Large +not Star) + (Large + Star + not Lemon) = 1 + 2 + 3 = 6

Total favorable possibilities = 1+6 = 7

P(atleast 2 features in cookie) = 7/24


C. 7/24
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There are 4 * 3 * 2 = 24 possible combinations of the features.

At least two -> it can be 3 or 2

Only 1 combination with exactly the same 3 features.

With 2 features:
Keep large and star-shaped features, different flavor: 3 possibilities (chocolate, vanilla or strawberry).
Keep large and lemon features, different shape: 2 possibilities (heart or circle).
Keep star-shaped and lemon features, different size: 1 possibility (small).

1 + 3 + 2 + 1 = 7

probability that the cookie picked has at least two of the three features Nina = 7/24

The correct answer is C
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probability (at least two of the three features) =
probability (same 3 features) + probability (exactly two of the three features) =
probability (same 3 features) + probablity (different flavor and same shape and size) + probablity (different shape and same flavor and size) + probablity (different size and same flavor and shape)

probability (same 3 features) = 1/4*1/3*1/2 = 1/24
probablity (different flavor and same shape and size) = 3/4*1/3*1/2 = 3/24
probablity (different shape and same flavor and size) = 2/3*1/4*1/2 = 2/24
probablity (different size and same flavor and shape) = 1/2*1/4*1/3 = 1/24

probability (at least two of the three features) = 1/24+3/24+2/24+1/24 = 7/24

The answer is C
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Let's translate the problem in the probability space:

At least 2 features ==> Exactly 2 features ( large + star, lemon + star , large + lemon) + Exactly 3 features ( large + star + lemon)

But we must be careful of eliminating the double countings:

P(large + star + lemon) = 1/24

P(large + star) = 4/24 ( 4 flavours possible) - here it's included also the option above
P(lemon + star) = 2/24 (2 sizes) - here also
P(large + lemon) = 3/24 (3 shapes) - here also

Total 7/24

IMO C!
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To pick at least 2 out of three features, the probability would be 1 - [Probability of none of the three + Probability of one of the three]

Total number of combinations = 4 flavours x 3 shapes x 2 sizes = 24 variants

Probability of none of the preferences = (3 flavours x 2 shapes x 1 size)/24 = 6/24

Probability of one of the preferences = Other lemon variants + other star variants + other large variants = (1x2x1)/24 + (1x3x1)/24 + (1x3x2)/24 = 11/24

=> answer = 1 - (6/24 + 11/24) = 7/24
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Total cases: 4*3*2=24

Favorable cases: 7
Same flavor, shape and size: 1
Same shape and size, different flavor: 3 (choosing any of the other 3 flavors)
Same flavor and size, different shape: 2 (choosing any of the other 2 shapes)
Same flavor and shape, different size: 1 (choosing the other size)

Probability = Favorable cases/Total cases = 7/24

Answer C
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Bunuel
A bakery sells cookies in four flavors: lemon, chocolate, vanilla, and strawberry. Cookies are made in three shapes: star, heart, and circle. Cookies also come in two sizes: small and large. The bakery has an equal number of cookies of each possible flavor-shape-size combination. Nina wants a large, star-shaped, lemon cookie. If her friend randomly picks one cookie from the display, what is the probability that the cookie picked has at least two of the three features Nina wants?

A. 1/24
B. 1/4
C. 7/24
D. 3/8
E. 17/24

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all 3 + large star not lemon + large lemon notstar + star lemon not large

1/4*1/3*1/2 + 1/3 * 1/2 * 3/4 + 1/2* 1/2 * 2/3 + 1/4*1/3*1/2

= 7/24
Correct Answer C
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Let us assume that one cookie of each kind is available (as the number of each kind of cpookie is not going to make a difference).
Then total number of cookies = 4*3*2 = 24

We need at least 2 out of the combination => Lemon+star+large.
=> All combination = 1
=> lemon+star and not large = 1
=> lemon+not star+ large = 2
=> not lemon+star+large = 3

At least 2 out of 3 = sum of all above = 1+1+2+3 = 7

Total proabability = 7/24 => C
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four flavors: lemon, chocolate, vanilla, and strawberry
three shapes: star, heart, and circle
two sizes: small and large

At least two features means 2 or 3 features.

3 features:
1/4 * 1/3 * 1/2 = 1/24

2 features, 3 cases:
different flavor, same shape and size: 3/4 * 1/3 * 1/2 = 3/24
different shape, same flavor and size: 1/4 * 2/3 * 1/2 = 2/24
different size, same flavor and shape: 1/4 * 1/3 * 1/2 = 1/24
3/24 + 2/24 + 1/24 = 6/24

Total: 1/24 + 6/24 = 7/24

IMO C
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The Bakery has an equal number of cookies for every combination of flavour , shape and size .
The Total number of unique type is calculated by multiplying the number of options for each category

Flavours : 4 (Lemon , Chocolate, Vanilla , Strawberry)
Shapes: 3 (Star , Heart, Circle)
Sizes: 2( Small , Large)
Total Combinations : 4x3x2=24

Nina wants a large (L) , Star shaped(St) , Lemon(Le) cookie. We need to find the number of cookies that have at least two of these features.

Exactly Two Features
1. Large and star (but not lemon): There are three other flavours . Outcome = 3
2. Large and Lemon (But not star) : There are 2 other shapes . Outcome = 2
3. Star and Lemon(But not large ) : There is one other size . Outcome = 1

Exactly 3 : Large , star and lemon : exactly 1 matches.

Total number of successful outcomes
3(exactly 2 ) + 2(exactly 2 ) + 1 ( exactly 2) + 1(exactly 3) = 7
Probability = 7/24 ✅
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