Problem Solving

5 people applied for 3 freshmen spots at a local business school. How many ways can the spots be filled?

Guys, please tell me what's the correct answer.
a. 10
b. 60
please elaborate your answer..

I would say its A.

You have 3 spots to be filled and you have 5 candidates. So you need find the number of ways you can choose 3 candidates out of 5.

5C3 = 5!/(3!2!) = 10 ways.

-BM-

bluementor wrote:I would say its A.

You have 3 spots to be filled and you have 5 candidates. So you need find the number of ways you can choose 3 candidates out of 5.

5C3 = 5!/(3!2!) = 10 ways.

-BM-

I would say it's B. It's the matter of filling 3 distinct spots by 3 distinct persons, we need to permute here, not combine.

5P3 = 5!/2! = 60.

Hi,

The answer is B.

Since it is asking for no. of ways its a problem based on permutation.

So it will be 5P3 which is 60.

bluementor wrote:I would say its A.

You have 3 spots to be filled and you have 5 candidates. So you need find the number of ways you can choose 3 candidates out of 5.

5C3 = 5!/(3!2!) = 10 ways.

-BM-

yeah, OA is A. Now could u please tell me what would be the answer to this question.. Also please lemme know the difference between the following question and the first question.

5 people are to be assigned to 3 different positions. How many ways can they be assigned?

For second answer

positions would be ABC and you need to select from 12345 (ppl).

1A 2B 3C is different from 1B 2A 3C so number of ways 5P3
5*4*3=60

However, for your first question

Postions would be AAA and persons are 12345
1A 2A 3A are same as 1A 2A 3A (well cant show you:D )

so total number of ways= 5P3 /3! ie 5C3= 10

ketkoag wrote:

bluementor wrote:I would say its A.

You have 3 spots to be filled and you have 5 candidates. So you need find the number of ways you can choose 3 candidates out of 5.

5C3 = 5!/(3!2!) = 10 ways.

-BM-

yeah, OA is A. Now could u please tell me what would be the answer to this question.. Also please lemme know the difference between the following question and the first question.

5 people are to be assigned to 3 different positions. How many ways can they be assigned?

In your second question, the 3 positions are different. So this means for a given set of 3 people choosen, there are 3! ways of assigning them to these positions.

The answer to second question will therefore be 5C3 x 3! = 60.

hope this helps.

-BM-

ketkoag wrote:5 people applied for 3 freshmen spots at a local business school. How many ways can the spots be filled?

Guys, please tell me what's the correct answer.
a. 10
b. 60
please elaborate your answer..

Is this an assumption question? When I first attempted this question, I thought I was dealing with unique positions. Will GMAT trick us with these kind of problems?

Could you please elaborate on this:

Postions would be AAA and persons are 12345
1A 2A 3A are same as 1A 2A 3A (well cant show you:D )

so total number of ways= 5P3 /3! ie 5C3= 10


I'm confused..

Whenever we interpret any quantitative logic in mind, what we speak to ourselves can be termed as our verbal ability. So, in a way we cannot separate the two abilities of ours, namely, quantitative and verbal, if we have to sail on either, to perfection. That’s why they say, “Weigh your words before you deliver”. The word ‘spot’ refers to a particular ‘point’, so this makes the word ‘a unique position’. 3 freshmen from 5 can be taken in, in 10 ways, no doubt about it; but each of these 10 ways would need to arrange the 3 entrees on the three “unique positions”. Why not? See these examples:

3 people are needed to sing a chorus from the available 5. In how many ways can the chorus be recorded?

10 ways! Why? Because who is playing back for whom on screen is not a matter here. On the other hand, if we rewrite the problem like this:

3 people are needed to sing for 3 actors on screen, from the available 5. In how many ways can the song be recorded?

60 ways! Any protest?

sanju09 wrote:Whenever we interpret any quantitative logic in mind, what we speak to ourselves can be termed as our verbal ability. So, in a way we cannot separate the two abilities of ours, namely, quantitative and verbal, if we have to sail on either, to perfection. That’s why they say, “Weigh your words before you deliver”. The word ‘spot’ refers to a particular ‘point’, so this makes the word ‘a unique position’. 3 freshmen from 5 can be taken in, in 10 ways, no doubt about it; but each of these 10 ways would need to arrange the 3 entrees on the three “unique positions”. Why not? See these examples:

3 people are needed to sing a chorus from the available 5. In how many ways can the chorus be recorded?

10 ways! Why? Because who is playing back for whom on screen is not a matter here. On the other hand, if we rewrite the problem like this:

3 people are needed to sing for 3 actors on screen, from the available 5. In how many ways can the song be recorded?

60 ways! Any protest?

I am in complete agreement with you Sanju. Quant & Verbal definitely go hand in hand. I observe that most of my mistakes in quant are either due to misinterpretation of the question or unable to comprehend what is being asked....& that automatically speaks for itself in the verbal section. I am struggling to get above 700 due to my weak verbal skills & mediocre quant score.

Coming back to the question, it says that there are 5 people (definitely unique) applied for 3 freshmen spots (order does not matter, they just need to filled). How many ways can the spots be filled? This is a combinations question. I completely missed it in my first attempt :roll:

Well, that means you do not agree with my answer, vemuri :roll:

sanju09 wrote:Well, that means you do not agree with my answer, vemuri :roll:

Well, I agree with you on the necessity to have good verbal skills to do well in Quant

As for the question, I have been deliberating it all afternoon. If the 3 people selected are A,B & C, the 3 freshmen spots can be filled as either ABC or BCA or CAB (which all mean the same). My understanding is that if the question does not specifically mention that order matters, we should always default to combinations. Any challenges to this argument?

getso wrote:Could you please elaborate on this:

Postions would be AAA and persons are 12345
1A 2A 3A are same as 1A 2A 3A (well cant show you:D )

so total number of ways= 5P3 /3! ie 5C3= 10


I'm confused..

Let say you contesting an election for secretary in same department and you have 3 vacant positions. YOu have 5 probable candidates.

So, total combination would be

5 for the first position
4 for the second postition
3 for the last position
=60 ways

Now we are interested in finding unique ways

60/3!=10

remember positions are same.

If positions are different say president, VP and secretary then
we will have 60 ways because 1 occupying the president position is different from 2 occupying the president's position.

Vemuri wrote:

sanju09 wrote:Well, that means you do not agree with my answer, vemuri :roll:

Well, I agree with you on the necessity to have good verbal skills to do well in Quant

As for the question, I have been deliberating it all afternoon. If the 3 people selected are A,B & C, the 3 freshmen spots can be filled as either ABC or BCA or CAB (which all mean the same). My understanding is that if the question does not specifically mention that order matters, we should always default to combinations. Any challenges to this argument?

What if the three people selected is a different group, other than your favorites: A, B, and C? I'm not agreeing with Hemant's stand as well, even if the three positions are of same capacity, but these are more importantly the three spots (read points, the three different addresses according to coordinate geometry) my dear friends!! Edit the wording of the question if you do not like B as answer I'm sorry... things are making me take life lightly with stretched smiles now...so please let me wind-up for now, see you guys on Monday...happy weekened...