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Question

A county commissioner will randomly select 5 people to form a non-partisan committee to look into the issue of county services. If there are 8 Democrats and 6 Republicans to choose from, what is the probability that the Democrats will have the more members than the Republicans on this committee?

A
6862002
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B
13162002
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C
18762002
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D
268824024
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E
2133624024
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Solution

The correct option is B 13162002

5 people need to be selected from 8 democrats and 6 republicans.

Democrats are more than republicans

5 democrats, 0 republicans 8C5

4 democrats, 1 republicans 8C4×6C1

3 democrats, 3 republicans 8C3×6C2=8C4×6C1+8C3×6C2+8C5=420+840+4856=1316

Total number of ways of selecting 5 people from 14 people =14C5

=14!5!×9!=2002

probability =13162002


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