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m05-183686.html#p1414023

Hey can I do this to solve the question
C(5, 3)+C(5, 1)+C(5, 1)

I feel like I need to work on permutation and combination form basic level can you guys help me figure out how to do it
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RITESH1984
https://gmatclub.com/forum/m05-183686.html#p1414023

Hey can I do this to solve the question
C(5, 3)+C(5, 1)+C(5, 1)

I feel like I need to work on permutation and combination form basic level can you guys help me figure out how to do it

I don’t think you need the other two, the (5,1) since there are three identical situations?

Also - if helpful:

21. Combinatorics/Counting Methods


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RITESH1984
Hey can I do this to solve the question
C(5, 3)+C(5, 1)+C(5, 1)
I don’t think you can.

When we say 5C3, that means -> selecting 3 DIFFERENT things from 5 DIFFERENT things.

For instance
-> selecting 2 people (different) from a group of 5 people -> 5C2

Here, 3 of the 5 things are the same Drama Movie. I don’t think we can do 5C3.

Solution -> here, we have the same drama movie 3 times, D,D,D; 1 action movie A; 1 comedy movie C.

We are asked to find the number of arrangements of these 5 movie screenings -> 5!/3!
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RITESH1984
Hey can I do this to solve the question
C(5, 3)+C(5, 1)+C(5, 1)
Your approach C(5, 3) + C(5, 1) + C(5, 1) is incorrect because you’re treating this as a sum of independent selections, which doesn’t reflect the structure of the problem.

If you were trying to solve it by selecting positions for each movie type, you’d need to use multiplication, not addition, because the cases are dependent. Specifically, you would do:

C(5, 3) * C(2, 1) * C(1, 1)

Where:

• C(5, 3): choose 3 slots for the drama movies
• C(2, 1): from the remaining 2 slots, choose 1 for the action movie
• C(1, 1): the last remaining slot goes to the comedy movie
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Bunuel
Your approach C(5, 3) + C(5, 1) + C(5, 1) is incorrect because you’re treating this as a sum of independent selections, which doesn’t reflect the structure of the problem.

If you were trying to solve it by selecting positions for each movie type, you’d need to use multiplication, not addition, because the cases are dependent. Specifically, you would do:

C(5, 3) * C(2, 1) * C(1, 1)

Where:

• C(5, 3): choose 3 slots for the drama movies
• C(2, 1): from the remaining 2 slots, choose 1 for the action movie
• C(1, 1): the last remaining slot goes to the comedy movie
Thanks that is what I was trying to do but because of lack of concepual and fundamental knowledge, I end up mixing every little things I know 🤣
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Problem Solving Butler: April 2025
April 23PS 1PS 2

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PS 1

In a certain box, the ratio of red marbles to blue marbles is 4 to 5, and the ratio of green to blue marbles is 2 to 3. What is the least number of marbles that could be present in the box?

A) 14
B) 15
C) 32
D) 37
E) 43

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PS 2

If \(a\) is equal to the product of positive even integers less than or equal to 18, and \(b\) is equal to the product of positive even integers less than or equal to 16, then what is the greatest prime factor of \(a-b\)?

A) 7
B) 11
C) 13
D) 17
E) 19
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Critical Reasoning Butler: April 2025
April 23CR 1CR 2

________________________________
CR 1

Along the mudflats of Garantia, exist two types of annelids: earthworms and lugworms. Earthworms tend to emerge from the mud early in the morning when there is more moisture and nutrients. As a result, earthworms have access to more nutrients and thus reproduce far faster than the lugworm, which spends much of the day submerged in the mud. Nonetheless, the lugworm population far outnumbers that of the earthworm.

Which of the following, if true, helps LEAST to resolve the apparent discrepancy noted above?

(A) Lugworms have specialized taste receivers, which allow them to access nutrients below ground far more easily than earthworms can.

(B) The whooping crane, the earthworm’s chief predator, hunts along the mudflats during the time the earthworms are feeding at the surface.

(C ) Lugworms resemble the color of the mudflat, and are thus more difficult to spot by predators than earthworms are.

(D) Compared to the lugworm, earthworms are able to consume fewer nutrients at one time.

(E) Lugworms tends to emerge in the evening, when the number of predators is less than during the early morning hours, when the earthworm is exposed on the mudflat.
________________________________
CR 2

GPS, the Global Positioning System (GPS) is a global navigation satellite system and is often used for navigating by car. Traveler's Best Friend (TBF) is a new navigation aids company which believes that not only drivers but also hikers could use GPS for navigating and have therefore decided to develop a GPS device for hikers.

Which of the following, if true, most seriously strengthens TBF's conclusion?

A. Technical problems prevent the entry of old mine fields data into the GPS device program.

B. A survey conducted by TBF shows that 82% of hikers would buy GPS hardware and software if the price is manageable.

C. Due to high developing prices, the price for the end purchaser is estimated at $15,000, far more expensive than any other single hiking accessory.

D. A rival company, TBP (traveler's best pal) has tried to develop the device, but were forced to halt the development due to technological limitations.

E. The estimated weight of the GPS system is roughly 40 pounds.
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Data Sufficiency Butler: April 2025
April 23DS 1DS 2

________________________________
DS 1

If Sarah was 21 years old exactly 5 years ago, how old was Larry exactly 9 years ago?

(1) Larry is now twice Sarah's age.

(2) Twelve years ago, Jill was 6 years older than Sarah and 20 years younger than Larry.
________________________________
DS 2

A women's track team has entered 15 athletes at an upcoming meet. Athletes will compete in running events, field events, or both. How many team athletes will compete in only running events?

(1) Four athletes will compete in running and field events.
(2) Seven athletes will compete in field events.
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