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805+ (Hard)|   Combinations|      
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Krunaal
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Sarah wants to buy two handbags from a store that offers 10 different 18 Mar 2025, 01:35
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C
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Difficulty:

95% (hard)

Question Stats:

20% (02:05) correct 80% (01:43) wrong based on 90 sessions

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Sarah wants to buy two handbags from a store that offers 10 different colors. Additionally, each handbag comes in three different sizes: small, medium, and large. How many different ways can Sarah choose her two handbags?

A. 435
B. 450
C. 465
D. 650
E. 900
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C
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Ertucinar
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Sarah wants to buy two handbags from a store that offers 10 different 18 Mar 2025, 01:57
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10 * 3 = 30 unique option for handbag
For 2 same and 2 different handbag selection
30C1 + 30C2 = 30 + 435 = 465 - Option C
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ToddlerandGMAT
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Sarah wants to buy two handbags from a store that offers 10 different 18 Mar 2025, 02:45
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Is there any good material to get clarity on when to apply permutation and when to apply combination? I'm getting confused with more questions i look into
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Sarah wants to buy two handbags from a store that offers 10 different 18 Mar 2025, 02:52
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[*]Permutation → Order matters
[*]Combination → Order doesn’t matter

Example:
  • Password Formation: Choosing 3 digits from {1,2,3,4} to form a password
    → Permutation (because "123" is different from "321")
  • Selecting a Team: Choosing 3 people from a group of 10
    → Combination (because "Alice, Bob, Charlie" is the same as "Charlie, Bob, Alice")
You don't always need to use the permutation formula explicitly; often it's enough to reduce the possibilities step by step and multiply them.
Example:
  • Password Formation: Choosing 3 digits from {1,2,3,4} to form a password
    → Permutation (because "123" is different from "321") 4P3 = 4!/(4-3)!
    → Reduce possibilities step by step and multiply = 4*3*2

Sangeeth217
Is there any good material to get clarity on when to apply permutation and when to apply combination? I'm getting confused with more questions i look into
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Sarah wants to buy two handbags from a store that offers 10 different 18 Mar 2025, 03:17
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Sangeeth217
Is there any good material to get clarity on when to apply permutation and when to apply combination? I'm getting confused with more questions i look into
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Would suggest to go through every sub-topic in this: https://gmatclub.com/forum/combinatoric ... 06266.html
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Sarah wants to buy two handbags from a store that offers 10 different 18 Mar 2025, 19:58
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Can someone explain why 30C1 would be a choice?

My answer was 435.

Is it because of replacement?
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Sarah wants to buy two handbags from a store that offers 10 different 18 Mar 2025, 22:28
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30C2 is for different unique bag options. (such as AB, AC, AD, BC, BD, CD)
30C1 should be added for unique options. (such as AA, BB, CC, DD)
There is no condition in the question that they should not be the same.
Khilji0007
Can someone explain why 30C1 would be a choice?

My answer was 435.

Is it because of replacement?
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Sarah wants to buy two handbags from a store that offers 10 different 19 Mar 2025, 02:00
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There are 30 unique handbags to choose from (3 sizes x 10 colors)

We have to select 2 from these 30.

We are not given in the question that these 2 selections need to be 2 distinct handbags, Sarah can select 2 handbags with same configuration (ex. 2 Large Red handbags)

Therefore, we will use the formula for combinations with repetition: \((n+r-1)C_r\) => \((30+2-1)C_2 = 31C_2 = \frac{(31*30)}{2} = 465\)

Answer C.
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