Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 25 May 2017, 03:48

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# There are 10 language professors, 4 of them teach only frenc

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Senior Manager
Joined: 22 Sep 2005
Posts: 276
Followers: 1

Kudos [?]: 208 [0], given: 1

There are 10 language professors, 4 of them teach only frenc [#permalink]

### Show Tags

27 Aug 2009, 07:36
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

There are 10 language professors, 4 of them teach only french, the rest teach only spanish or german. How many groups of 3 teachers with at least 1 french teacher can be formed?
Manager
Joined: 10 Jul 2009
Posts: 166
Followers: 2

Kudos [?]: 106 [0], given: 8

Re: There are 10 language professors, 4 of them teach only frenc [#permalink]

### Show Tags

27 Aug 2009, 07:47
Number of ways of selecting the group of 3 with atleast one French teacher =
= 6c2*4c1 + 6c1*4c2 + 6c0*4c3
= 60 +36 + 4 = 100
Manager
Joined: 20 Aug 2009
Posts: 105
Followers: 2

Kudos [?]: 128 [0], given: 31

Re: There are 10 language professors, 4 of them teach only frenc [#permalink]

### Show Tags

28 Aug 2009, 05:23
Agree with Aleehsgonji (i nearly broke my finger typing you nickname )))) Just want to add a little bit of explanation.

The possible arrangements are:

1) One F AND two S/G, OR
2) Two F AND one S/G, OR
3) Three F

1) We choose one French professor out of four French professors AND (which means that we should multiply the number of ways in which we can arrange french and spanish/german professors) we choose two S/G professors out of six S/G professors (10 - 4 French = 6 S/G). Translating into mathematical symbols, we get: 1C4*2C6
2) Similarly, we construct the equation for possible arrangement 2): 2C4*1C6
3) 3C4

Since either of the arrangements is possible (see OR, which means that we should sum all the arrangements), the final equation looks like:
1C4*2C6+2C4*1C6+3C4

_______________________
Please kudos me if you find my post useful
Manager
Joined: 18 Jul 2009
Posts: 169
Location: India
Schools: South Asian B-schools
Followers: 2

Kudos [?]: 105 [0], given: 37

Re: There are 10 language professors, 4 of them teach only frenc [#permalink]

### Show Tags

28 Aug 2009, 05:56
atleast one french prof means (1F+2S/G) OR (2F+1S/G) OR (3F)
4C1*6C2 + 4C2*6C1 + 4C3 = 100
_________________

Bhushan S.
If you like my post....Consider it for Kudos

Manager
Joined: 25 Aug 2009
Posts: 175
Followers: 1

Kudos [?]: 91 [0], given: 12

Re: There are 10 language professors, 4 of them teach only frenc [#permalink]

### Show Tags

29 Aug 2009, 06:47
Atleast 1 french means = total - no french
= 10C3 - 6C3
= 120 - 20 = 100
Manager
Joined: 14 Aug 2009
Posts: 123
Followers: 2

Kudos [?]: 105 [0], given: 13

Re: There are 10 language professors, 4 of them teach only frenc [#permalink]

### Show Tags

29 Aug 2009, 09:23
gmate2010 wrote:
Atleast 1 french means = total - no french
= 10C3 - 6C3
= 120 - 20 = 100

yep, this one is quicker.
_________________

Kudos me if my reply helps!

Senior Manager
Joined: 22 Sep 2005
Posts: 276
Followers: 1

Kudos [?]: 208 [0], given: 1

Re: There are 10 language professors, 4 of them teach only frenc [#permalink]

### Show Tags

31 Aug 2009, 14:30
You are right.
Oa is 100
Re: There are 10 language professors, 4 of them teach only frenc   [#permalink] 31 Aug 2009, 14:30
Display posts from previous: Sort by

# There are 10 language professors, 4 of them teach only frenc

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.