From 12 mobile sets, how many ways are there to select 5 mob

Question

From 12 mobile sets where 3 mobile sets are identical , how many ways are there to selecet 5 mobile sets ?

a) 136
b) 162
c) 372
d) 36
e) none

Different sources say different answer. Plz someone clarify this one.

Posted from my mobile device

road740 · Answer

Where did you find this one?

My solution is 252, under the assumption that we choose "5  different  mobile sets".

If we have 12 differents mobile sets and 3 of them are identical, then we have 10 sets that differ from each other. From these sets we need to choose 5.
--> no order
--> no repitition
--> (n,k)

So we have: (10,5) = (10!/(5!*5!)) = 252.

Please correct me if I´m wrong!

Regor60 · Answer

Select 0 from identical set, 5 from distinct 9

9!/5!4! = 126

Select 1 from identical set, 4 from distinct

3!/1!2! * 9!/4!5! = 378

Note that there are 3 ways to select 1 object from the identical because there exist 3 physical objects despite their identical appearance. 
Also keep in mind the question isn't asking for distinct arrangements.

Select 2 from identical set, 3 from set of 9

3!/2!1! * 9!/3!6! = 252

Select 3 from identical, 2 from 9

1 * 9!/7!2! = 36

Total Ways = 792

Posted from my mobile device

IanStewart · Answer

These questions where answer E just says "none" aren't GMAT questions -- they're either official questions or prep material questions for a standardized math test in India, and many of these questions are not within GMAT scope. This question is also badly worded, because it's unclear what would constitute a "way" to select 5 mobile sets (and I don't even know what a "mobile set" is

). If you have 3 people, and a question asks "how many ways can you select a team of 2", one way might be "select the two tallest people" and another might be "select two people randomly" and another might be "select the first two people alphabetically". The answer is infinite. What the question means to ask is: "how many different selections are possible?" We can divide the problem into cases: • if we choose none of the identical sets, we'll be choose 5 sets from 9, and we have 9C5 options • if we choose one of the identical sets, we know one of our items already, and need to choose 4 of the remaining 9, and we have 9C4 options (you could actually combine this case with the first if you like, and just count the possibilities where you use at most one of the identical sets -- then you get 10C5, which is equal to 9C5 + 9C4) • if we choose two of the identical sets, we know two items already, and need to choose 3 of the remaining 9, for 9C3 options • if we choose all three of the identical sets, we're choosing only 2 of the remaining 9, for 9C2 options So the answer is 9C5 + 9C4 + 9C3 + 9C2 = 126 + 126 + 84 + 36 = 372. If the answer "none" didn't appear among the choices, you could get the answer without really doing much work. If all the sets were different, we'd have 12C5 = 792 options. The repetition will reduce the number (if it's not clear why repetition reduces the total number of possible selections, imagine all the sets were identical -- then we'd have just one possible selection). But if we ignore the possibility that we choose 2 or more identical sets, we have 10C5 = 252 possible selections, and since we might also choose 2 or 3 identical sets, the answer must be larger than that. Only one answer choice (besides "none") is left.

road740 · Answer

Got it, thanks!

Regor60 · Answer

I'd stick with the approach above which yields 372.

I've seen arguments for/ against my interpretation and the usual way the question is intended is as Ian describes

itskAKku · Answer

Well ... i got 132... thus E.

Selecting 5 from 12 with 3 identical...

So its (12!)/(((12-5)! * 5!) * 3!) or if ur familier with c n all so its 12c5/3!
 
which results 132.. if im not wrong ...

AbhishekP220108 · Answer

Bunuel  can you please change the answer choice to C? If it's correct. Check the expert solution, as I am also getting 372. I don't know how it's 36.

36 is only possible if the three identicals are getting selected and the other 2 from the remaining 9.

Bunuel · Answer

The topic is archived.

From 12 mobile sets, how many ways are there to select 5 mob

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