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# Gmat prep source - counting

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Manager
Joined: 30 Dec 2008
Posts: 121
Gmat prep source - counting [#permalink]

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12 Jan 2009, 21:59
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in a certain group of 10, 4 members teach french only, 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
Manager
Status: Stanford GSB
Joined: 02 Jun 2008
Posts: 94
Re: Gmat prep source - counting [#permalink]

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12 Jan 2009, 22:59
Total number of 3 member subcomitees = 10C3 = 120

Total number of subcomitees that can be formed from ONLY Spanish or German = 6C3 = 20

at least 1 member who teaches French = 120 - 20 =100

Another technique ( slighly longer)

a)1 French + 2 others
1 French = 4
2 others = 6C2 = 15
Total = 15 * 4 = 60

b) 2 F + 1 O
2F = 4C2 = 6
1O = 6
Total = 6*6 = 36

c) 3 F
= 4C3 = 4

So total number of ways = 60 + 36 + 4 = 100
Manager
Joined: 30 Dec 2008
Posts: 121
Re: Gmat prep source - counting [#permalink]

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12 Jan 2009, 23:11
wonderful explanation. THanks !
Director
Joined: 14 Aug 2007
Posts: 726
Re: Gmat prep source - counting [#permalink]

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12 Jan 2009, 23:18
all 3 french : 4C3
+(OR)
2 french AND 1 from spanish/german: 4C2*6C1
+(OR)
1 French AND 2 from spanish/german: 4C1*6C2
Re: Gmat prep source - counting   [#permalink] 12 Jan 2009, 23:18
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# Gmat prep source - counting

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