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

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.

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 ?

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.

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.