A five-person team is to be formed from a pool of 6 East All Stars and

Question

A five-person team is to be formed from a pool of 6 East All Stars and 6 West All Stars. What is the probability that the team will contain at least 2 East All Stars?

A. 29/33
B. 81/169
C. 57/120
D. 47/144
E. 119/720

RDhin · Accepted Answer

A five-person team is to be formed from a pool of 6 East All Stars and 6 West All Stars. What is the probability that the team will contain at least 2 East All Stars?

The question with at- least can be easily tackled by 
At least = Total cases - unwanted cases

So atleast 2 player = total cases - cases with no east all stars person - case with only one east all person

Total number of cases =  12C5 = 798

Cases with no east all person =  6C5(All person from west all stars) = 6 
Cases with exactly one east all person =  6C4*6C1 (4from west all stars and 1 from east all stars)= 90

So total no. of cases with with atleast two members = 798-6-90 = 702
 
Probability = 702/798 = 29/33

Skywalker18 · Answer

Teams can be formed as 2E-3W , 3E-2W , 4E-W and 5E
Possible ways to make a team 2E-3W = 6c2 * 6c3 = 300
Possible ways to make a team 3E-2W = 6c3 * 6c2 = 300
Possible ways to make a team 4E-W = 6c4 * 6c1 = 90
Possible ways to make a team 5E = 6c5 = 6

Number of ways to select a team of 5 out of 12 people = 12c5
=12!/(7!*5!)
= 792

Probability that the team will contain at least 2 East All Stars
= (300+300+90+6) / 792
=696/792
= 29/33

Answer A

Alternatively we can also calculate the number of possible ways to make a team of 5W and E-4W .
Possible ways to make a team 5W = 6c5 = 6
Possible ways to make a team E-4W = 6c1 * 6c4 = 90

Probability that the team will contain at least 2 East All Stars = 1 - (96/792)
= 29/33

Shruti0805 · Answer

Hi Bunuel , Math Experts, Ive been trying to find a pattern to understand when do we need to multiply the counts by the number of arrangements and when not to. For example, in this question, while counting the probability of selecting a team that contains 3 east all stars and 2 west all stars, what I did was : \frac{6C3*6C3}{12C3} * \frac{5!}{3!*2!} Similarly, I counted the numbers for a team with 2 east all stars, 4 east all stars and all 5 east all stars. Can you please help understand the concept ? For ex., why did we multiply by the no. of arrangements in qsn : https://gmatclub.com/forum/there-are-8- ... 92342.html but not in the current one ?

DharLog · Answer

It is sometimes really good thing to check options fist.
For ex in this case we could save us a lot of time.

All these probabilities except that one in A are less than 1/2. It just can't be. So the answer is A 
Why? How many players from East can be in our command? 0, 1, 2, 3, 4, or 5.
Which ones fit in our case? 2, 3, 4, 5- it is definetely more than and 1.
(We know that 6C6 = 6C0, 6C5 = 6C1 and so on).
So the probaility will be decently greater than 1/2.

Trent981 · Answer

In reality, This is a poor quality question. Once you realize that denominator has to have a multiple of 11 which is missing in all other options - then you know option A has to be the only answer.

ThatDudeKnows · Answer

Trent981

Two things.

First, what about that observation makes you believe that it is a poor quality question? That is EXACTLY the type of thing GMAC does on questions. If someone feels compelled to work through the math, have a great time; they'll get to the right answer. But if someone can spot a path to the finish line that avoids the math, that's just as valid (I'd argue that it is MORE valid given the purpose of the GMAT). Have you noticed that the section is called "Quantitative Reasoning," not "Quantitative?" Business schools couldn't care less whether you can do permutations and combinations. They are not looking for the next amazing high school math teacher; they are looking for the next tycoons of business. Those people tend to be less about nCr than they are about finding creative solutions, thinking outside the box, and identifying what's important and what's not. This question is a GREAT example.

Second, what if I told you there's an even easier way than the one you identified? 
We have an equal number of Es and Ws and need to pick five. Aren't more than half of the arrangements going to contain at least two Es? Only one answer choice is >50%. 
Answer choice A.

e3thekid · Answer

At least 2 East All stars can mean a few different scenarios given the information in the question stem.

Total Pool: 6 East All Stars and 6 West All Stars

Out of a five-person team, we can have:

2 East All Stars and 3 West All Stars OR

3 East All Stars and 2 West All Stars OR

4 East All Stars and 1 West All Star OR

5 East All Stars

Using the probability formula: 
Favorable cases/ Total Cases

P(First Scenario) : 
2 East and 3 West

6C2 x 6C3 / 12C5 =
15 x 20 / 792 = 300 / 792

P(Second Scenario) :
3 East and 2 West

6C3 x 6C2 / 12C5 =
20 x 15 / 792 = 300 / 792

P(Third Scenaro) : 
4 East and 1 West

6C4 x 6C1 / 12C5 =
15 x 6 / 792 = 90 / 792

P(Fourth Scenario) :
5 East

6C5 / 12C5 =
6 / 792

Probability of At Least 2 East All Stars =
P(first) + P(second) + P(third) + P(fourth)

300/792 + 300/792 + 90/792 + 6/792 =

696/792 which simplifies to 29/33

Option A

Posted from my mobile device

Kinshook · Answer

Given: A five-person team is to be formed from a pool of 6 East All Stars and 6 West All Stars.

Asked: What is the probability that the team will contain at least 2 East All Stars?

Total cases = 12C5 = 792
Favorable case = 6C2*6C3 + 6C3*6C2 + 6C4*6C1 + 6C5*6C0 = 15*20 + 20*15 + 15*6 + 6 = 696

The probability that team will consist of at least 2 East All Stars = 696/792 = 29/33

IMO A

Posted from my mobile device

A five-person team is to be formed from a pool of 6 East All Stars and

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A five-person team is to be formed from a pool of 6 East All Stars and

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards