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GMAT Prep Software Question

Expert replies
by awilhelm » Fri Dec 12, 2008 7:51 pm
Could anyone explain how to approach this? Thanks in advance.

In a certain group of 10 members, 4 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
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Source: — Problem Solving |

by cramya » Fri Dec 12, 2008 8:06 pm
One of the easier ways would be to calculate all possible 3 memeber subcomittess from 10 and then subtratc from it the total number of subcomittees possible 3 memeber subcomittess with no french(from the 6 that are spanish and german)

Total number of 3 member subcomitees that can be formed from 10 = 10C3 = 120

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

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

Choose E)
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by awilhelm » Fri Dec 12, 2008 8:35 pm
Thanks!
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by acecoolan » Sat Dec 13, 2008 5:18 pm
The other way would be the longer way

Problem says ..at least 1 ..so the options are
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
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