probability

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divya23: Master | Next Rank: 500 Posts; Posts: 113; Joined: Mon Apr 26, 2010 8:58 amFollowed by: 14 members; Thanked: 2 times

by divya23 » Mon Jun 06, 2011 10:23 am

18 applicants are to be selected for 4 postions.how many different gropus of 4 applicants can be chosen by caomany to fill the postion if order dies not matter...

[spoiler]ans = 3060[/spoiler]

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Source: Beat The GMAT — Problem Solving | Mon Jun 06, 2011 10:23 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Mon Jun 06, 2011 10:39 am

Hi,
Number of ways of selecting 4 from 18 is 18C4 = 3060.

Cheers!

Things are not what they appear to be... nor are they otherwise

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Mon Jun 06, 2011 4:45 pm

18 people. select 4
Thus 18C4 = 18*17*16*15/24 = 3060

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davo45: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Tue Nov 23, 2010 5:11 pm; Location: Beijing, China; Thanked: 1 times

by davo45 » Mon Jun 06, 2011 5:57 pm

Thanks for the reasoning Cans. Please refresh my memory and tell me why the figure is divided by 24 and not 18.

Thanks.

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Whitney Garner: GMAT Instructor; Posts: 273; Joined: Tue Sep 21, 2010 5:37 amFollowed by: 74 members; Location: Durham, NC; Thanked: 154 times; GMAT Score:770

by Whitney Garner » Mon Jun 06, 2011 6:45 pm

davo45 wrote:Thanks for the reasoning Cans. Please refresh my memory and tell me why the figure is divided by 24 and not 18.

Thanks.

For combinations, the formula is:

nCr (from n choose r)

n!/[r!(n-r)!] = 18!/[4!14!] = (18*17*16*15)/(4*3*2*1)

Whit

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Mon Jun 06, 2011 6:49 pm

it's the combination formula: n!/r! (n-r)!

18! / 4! (18-4)! = 18*17*16*15/ 4*3*2*1 = 73440/24 = 3060

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Mon Jun 06, 2011 8:00 pm

davo45 wrote:Thanks for the reasoning Cans. Please refresh my memory and tell me why the figure is divided by 24 and not 18.

Thanks.

24 is 4! and 18C4 means 18! / (4! * 14!) =

If my post helped you- let me know by pushing the thanks button

Contact me about long distance tutoring!
[email protected]

Cans!!

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[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Fri Jun 10, 2011 3:46 am

was this sentence is used to indicate that this is an combinations sum:

.how many different gropus of 4 applicants can be chosen by caomany to fill the postion if order dies not matter...

I just got a little confused and so please help me get rid of this confusion..

IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Fri Jun 10, 2011 3:58 am

[email protected] wrote:was this sentence is used to indicate that this is an combinations sum:

.how many different gropus of 4 applicants can be chosen by caomany to fill the postion if order dies not matter...

I just got a little confused and so please help me get rid of this confusion..

Hi,
how many different gropus of 4 applicants can be chosen by company to fill the position.
Choosing means selection(combination).

Order comes into play only when we talk about arrangement(permutation).

Cheers!

Things are not what they appear to be... nor are they otherwise

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Fri Jun 10, 2011 11:07 am

Frankenstein wrote:
[email protected] wrote:was this sentence is used to indicate that this is an combinations sum:

.how many different gropus of 4 applicants can be chosen by caomany to fill the postion if order dies not matter...

I just got a little confused and so please help me get rid of this confusion..
Hi,
how many different gropus of 4 applicants can be chosen by company to fill the position.
Choosing means selection(combination).

Order comes into play only when we talk about arrangement(permutation).

It is not the word 'chosen' that indicates we are dealing with a combination -- that is, that order does not matter. It is the fact that we are selecting 'groups' that tells us that the order of the people doesn't matter -- you still have the same group of people no matter what order you put them in.

There are many counting questions which use the word 'choose' but where order does matter. For example, I could ask how many ways you could choose a President and Treasurer from a group of 8 people. Then the order of the two selections clearly does matter, since if you change the order of the two people you select, you get a new President.

The word 'choose' has a technical definition in advanced math, but that definition sometimes conflicts with the way the word is used in day-to-day speech, and sometimes conflicts with the way the word is used on the GMAT. For GMAT purposes, it's best to forget the mathematical definition of the word 'choose' -- you should not assume, when you see the word 'choose' in a GMAT question, that order does not matter.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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