12 Days of Christmas GMAT Competition 2025 - Day 10: A bakery sells

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Bunuel

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26 Dec 2025, 10:00

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Bunuel

GMAT Club Official Explanation:

Total equally likely cookies = 4 * 3 * 2 = 24.

Nina wants lemon, star, large.

Count cookies that match at least two of these:

All three features:
• 1 cookie (large, star-shaped, lemon cookie).

Exactly two features:
• Star and large but not lemon: 3 cookies (chocolate, vanilla, or strawberry.).
• Lemon and large but not star: 2 cookies (heart, or circle.).
• Lemon and star but not large: 1 cookie (small).

So exactly two = 3 + 2 + 1 = 6.

At least two = 6 + 1 = 7.

Probability = 7/24.

Answer: C.

General Discussion

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26 Dec 2025, 09:10

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Bunuel

total possible outcomes = 4 * 3 * 2 = 24

all 3 features =1
any 2 features =
matching shape size = 3
size flavor = 2
flvor shape = 1
total = 7

ans is 7/24

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26 Dec 2025, 09:19

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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

total ways to choose a cookie
4 flavors ; 3 shapes ; 2 sizes
4*3*2 ;24

Nina wants cookie
large, star shaped , Lemon
at least two of three features
all three features
1*1*1 =1
possible options
Lemon , large , ( heart & circle )
1*1*2 = 2
Lemon , star , large = 1 *1*1 = 1
Star , large , not lemon = 1*1*3 = 3
7 ways
7/24 is at least 2 features

OPTION C ; 7/24

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26 Dec 2025, 09:25

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With given conditions there are 4 x 3 x 2 = 24 cookies.
Atleast two means 2 or all 3 features.
With all three features of large, star shaped and lemon there is only 1 cookie = 1/24
With any two
i) there are 3 large, star shaped cookies without lemon flavour
ii) there are 2 large, lemon cookies other than star shaped
iii) there is only 1 small, star shaped lemon cookie

hence choosing cookie with 2 preferences = 6/24

Hence total probability is = 7/24 Option C

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26 Dec 2025, 09:28

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no of choices is 4x3x2=24
large star shaped and lemon

atleast 2 is required
large star shaped: 3
large lime :2
star shaped lime:2
3+2+2/24=7/24 is the answer

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26 Dec 2025, 09:31

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Total combinations = 4 * 3 * 2 = 24

Cookie with 2 features = 3*1*1 + 1*2*1 +1*1*1 = 3+2+1 =6
Cookie with all 3 = 1
Cookie with at least 2 features = 6+1 = 7

P(Cookie with atleast 2) = 7/24

Bunuel

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26 Dec 2025, 09:42

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Bunuel

Total equally likely cookies: 4(flavors) x 3(shapes) x 2(sizes) = 24

"At least 2 features": (all 3 match) + (exactly 2 match)

All 3 match: 1 cookie (large + star + lemon)

Exactly 2 match: wrong flavor(3 ways, for ex: ( chocolate,star,large), (vanilla,star,large), (strawberry,star,large))+ wrong shape(2 ways, ex: (lemon, large, heart), (lemon,large,circle)) + wrong size(1 way, ex: (lemon,star, but small size)) = 6

Total favorable = 1 + 6 = 7

probability = 7/24

Option C

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26 Dec 2025, 10:02

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A bakery sells cookies in 4 flavors: lemon(l), chocolate(ch), vanilla(v) and strawberry(sy)
Cookies are made in three shapes: star(s), heart(h) and circle(c)
Cookies come in two sizes: small(S) & large(L).

Total possible combinations = 4*3*2 = 24 combinations
Since the probability is the ratio of 2 numbers, let us assume that there is 1 cookie of each type.

Nina wants a large, star-shaped, lemon cookie (l-s-L)

The number of cookies with all 3 features (l-s-L)= 1
The number of cookies with 2 of 3 features = {l-s-S, ch-s-L, v-s-L, sy-s-L, l-h-L, l-c-L} = 6

The number of cookies with at least 2 of the 3 features = 1 + 6 = 7

The probability that the cookies has at least 2 of the 3 features Nina wants = 7/24

IMO C

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26 Dec 2025, 10:09

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flavor= l,c,v,s
shape= s,h,c
size= s,l

total 24 combinations
p(2 feature) + p (3 feature)
6/24 + 1/24
7/24

Bunuel

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26 Dec 2025, 10:22

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Total number of cookie combinations = 4 flavours * 3 shapes * 2 sizes = 24

The number of combinations will all three features matched = 1
The number of combinations with 2 out of 3 features matched can be found in
3C2 = 3ways

For each case, the other features are different.
When flavour is anything but lemon, there are 3C2 = 3 ways to choose flavour
when shape is anything but star, there 2C1 = 2 ways to choose the shape
when the size is anything but large, there is 1 way to choose

Counting the total number of combinations with atleast 2out of 3 matched features
= 1 + 3 + 2 + 1 = 7

Probability that the cookie picked has atleast 2 out of 3 features matched = 7/24

Bunuel

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26 Dec 2025, 10:26

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Bunuel

Total Possible Cases = 4 * 3 * 2 = 24

Atleast 2 = Total - (Only 1 + None)

Total = 24

Only 1 = Flavor matches but not size or shape + Size matches but not flavor and shape + Shape matches but not size and flavor

= 2 * 1 + 3 * 1 + 2 * 3 = 11

None = Either flavor, shape not size matches = 3 * 2 * 1 = 6

Atlteast 2 = 24 - (11+6) = 7

Probability = 7/24

Option C

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26 Dec 2025, 10:36

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4 flavors = L,C,V,S
3 shapes = Star, Heart, Circle
2 sizes = Large, Small
Total number of distinct type of cookies= 4*3*2=24

Nina wants Lemon, Star, Large
Gets all 3 features (Large, Star, Lemon) = 1 combination
Gets exactly 2 features of= (Flavour, shape but not size) 1 combination + (Flavour size but not shape - Lemon heart large or lemon circle large) 2 combination + (Shape size but not flavour- Chocolate star large , vanilla star large, strawberry star large) 3 combinations =6 combinations

Probability her friend gets atleast 2 features of desired 3 = 1+6=7
Required probability =7/24

C

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26 Dec 2025, 10:56

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Bunuel

You can consider flavour, shape and size as different "slots" that need to be filled, so we use counting principle for identifying the total number of options possible. Note that order doesn't matter here.

$Total=4*3*2=24$

We're asked for at least two parameters matching. So we have two cases: all three parameters match, and only two parameters match.

Case 1: There is only 1 option for this.
Case 2: If cut and size are same, there are 3 options for flavour. If flavour and size are the same, there are 2 options for cut. If flavour and cut are the same, this 1 option for size.

Summing this up we get:
$1+2+3+1=7$

Therefore probability is $\frac{7}{24}$, answer is C.

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26 Dec 2025, 11:36

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Prob (X>=2)=1-P(X=0)-P(X=1)
X=0 means NO_LARGE,NO_STAR,NO_LEMON
X=1 means (Large only) OR (STAR only) OR (Lemon Only)
=1-(1/2 * 2/3 *3/4)-((1/2*2/3*3/4)+(1/2*1/3*3/4)+(1/2*2/3*1/4))
=7/24

Ans 7/24

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26 Dec 2025, 11:46

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The total possible combinations are 4 flavors * 3 shapes * 2 sizes = 24

you need to find the probability of 2 features matching + the probability of all 3 features matching.

P(Lemon and Star and Large) = 1/24
P(Lemon and Star) = 1/24 -> there is only 1 other possible size
P(Lemon and Large) = 2/24 -> there are 2 other possible shapes
P(Star and Large) = 3/24 -> there are 3 other possible flavors

the sum is 7/24

Answer C

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26 Dec 2025, 12:04

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Lemon, Choco, Vanilla, Strawberry

Star, Heart, Circle

Small, Large

Total number of possibilities: 4 * 3 * 2 =24

Exactly 2: (flavor & shape & not size) or (flavor & not shape & size) or (not flavor & shape & size)

(1 * 1 * 1) + (1 * 2C1 * 1) + (3C1 * 1 * 1)
1 + 2 + 3
= 6

all 3: (flavor & shape & size)
(1 * 1 * 1)
= 1

Atleast 2 = 6 + 1 = 7

ans: $\frac{7}{24 }$

another way: 1 - prob of none - prob of exactly 1

none: (not flavor and not shape and not size)
3C1 * 2C1 * 1C1
3 * 2 * 1
= 6

exactly 1: (flavor and not shape and not size) or (not flavor and shape and not size) or (not flavor and not shape and size)
(1 * 2C1 * 1) + (3C1 * 1 * 1) + (3C1 * 2C1 * 1)
2 + 3 + 6
= 11

$1 - \frac{(6+11) }{ 24}$

$1 - \frac{17}{24} $

ans: $\frac{7}{24}$

ans: Option C

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26 Dec 2025, 12:17

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cookie flavors--> lemon, chocolate, vanilla, strawberry=4
cookie shapes-->star, heart, circle=3
cookie sizes-->small, large=2
so total different combinations for cookies=4*3*2=24
now Nina wants a large star shaped lemon flavored cookie.
so to find out Probability(one cookie picked at random has at least 2 of the 3 features Nina wants)=?
means it can have two or all the three features.
now for a lemon-star shaped cookie has 2 choices for sizes (small or large) OR
a lemon large cookie has 3 choices for shapes (star, heart or circle) OR
a large star cookie has 4 choices for flavor (lemon, chocolate, vanilla or strawberry)
so a total of 09 choices.
but in the above process we have counted the requirement i.e. large lemon star cookie thrice.
so favorable no of choices=9-2=7
so required probability=7/24

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26 Dec 2025, 14:09

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	lemon	chocolate	vanilla	strawberry
star (small)	1	1	1	1
star(large)	1	1	1	1
heart (small)	1	1	1	1
heart(large)	1	1	1	1
circle(small)	1	1	1	1
circle(large)	1	1	1	1

total cookies= 4x3x2=24
possible outcome (atleast 2 of large,star,lemon)= 7
prob=7/24

Bunuel

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26 Dec 2025, 14:12

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Bunuel