It is currently 24 Nov 2017, 01:07

### 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

# In a certain group of 10 members, 4 members teach only

Author Message
Manager
Joined: 17 Aug 2005
Posts: 165

Kudos [?]: 297 [0], given: 0

In a certain group of 10 members, 4 members teach only [#permalink]

### Show Tags

18 Oct 2005, 09:08
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose a 3-member committee, which must have at least 1 member who teaches French, how many different committees can be chosen?

(A) 40
(B) 50
(C) 64
(D) 80
(E) 100

Kudos [?]: 297 [0], given: 0

VP
Joined: 22 Aug 2005
Posts: 1111

Kudos [?]: 124 [0], given: 0

Location: CA

### Show Tags

18 Oct 2005, 09:28
E. 100

Possible combinations are:
1F & 2 Others
2F & 1 Other
3F & 0 Other

total combinations:
4c1 * 6c2 + 4c2 * 6c1 + 4c3 * 6c0 = 100

Kudos [?]: 124 [0], given: 0

Director
Joined: 14 Oct 2003
Posts: 582

Kudos [?]: 59 [0], given: 0

Location: On Vacation at My Crawford, Texas Ranch

### Show Tags

18 Oct 2005, 09:36
kimmyg wrote:
In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose a 3-member committee, which must have at least 1 member who teaches French, how many different committees can be chosen?

(A) 40
(B) 50
(C) 64
(D) 80
(E) 100

Easiest and shortest way to solve a combination with a constraint is to

First Find the Total Combination w/o constraints

10 C 3 = 120

Find the Combination of NO French teachers 6 C 3 = 20

Subtract the the Combination of having no French teachers from the total

10C3-6C3=100

Less than 1.5 mins.

Kudos [?]: 59 [0], given: 0

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5032

Kudos [?]: 453 [0], given: 0

Location: Singapore

### Show Tags

18 Oct 2005, 09:37
We're given:

French - 4 members
Spanish or German - 6 members

The group of three must have at least 1 member who teaches French:

Three cases:

Case 1: 2 French member and 1 Spanish or German

4C2*6C1 = 36 combinations

Case 2: 1 French member and 2 Spanish or German
4C1*6C2 = 60 combinations

Case 3: 3 French members
4C3 = 4 combinations

Total = 100 combinations

Kudos [?]: 453 [0], given: 0

18 Oct 2005, 09:37
Display posts from previous: Sort by

# In a certain group of 10 members, 4 members teach only

Moderator: chetan2u

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.