SOLUTION: Can you please help me with this problem? Consider a political discussion group consisting of 4 democrats, 7 republicans and 5 independents. Suppose that 2 group members are rando

Algebra ->  Permutations -> SOLUTION: Can you please help me with this problem? Consider a political discussion group consisting of 4 democrats, 7 republicans and 5 independents. Suppose that 2 group members are rando      Log On


   

Question 1071310: Can you please help me with this problem?
Consider a political discussion group consisting of 4 democrats, 7 republicans and 5 independents. Suppose that 2 group members are randomly selected in succession, to attend a political convention. Find the probability of selecting 2 independents.

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Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There are %28matrix%282%2C1%2C5%2C2%29%29=5%2A4%2F2=10 different
pairs of independent discussion group members
that could happen to be selected to attend the convention.
That number is combinations of 5 taking 2 at a time.
The entire discussion group is made of 4%2B7%2B5=16 members.
From that group, the number of different possible member pairs is
%28matrix%282%2C1%2C16%2C2%29%29=16%2A15%2F2=120 .
That number is combinations of 16 taking 2 at a time.
Since only 10 of those 120 pairs have 2 independent members,
the probability of that happening is
10%2F120=highlight%281%2F12%29 .