SOLUTION: In a class of 12 boys and 8 girls, a committee of three should be formed. What is the probability that there are at least two girls on the committee?

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Question 1120232: In a class of 12 boys and 8 girls, a committee of three should be formed. What is the probability that there are at least two girls on the committee?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The P( 2 or more girls on committee of 3 ) is
1 minus P( no girls on committee AND 1 girl on committee )
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The number of possible committees formed with no girls is:
C( 12, 3 ) = +12%21+%2F+%28+%28+12+-+3+%29%21+%2A+3%21+%29+
+12%21+%2F+%28+9%21+%2A+3%21+%29+=+%28+10%2A11%2A12+%29+%2F+%28+3%2A2+%29+
+10%2A11%2A2+=+220+
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Possible committees with 1 girl is:
C( 12, 2 )*8 = +%28+12%21+%2F+%28+10%21+%2A+2%21+%29%29+%2A+8+
+%28%28+11%2A12+%29+%2F+2+%29+%2A+8+
+66%2A8+=+528+
and
+220+%2B+528+=+748+
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the total possible committees is:
C( 20, 3 ) = +20%21+%2F+%28+17%21+%2A+3%21+%29+
+%28+18%2A19%2A20+%29+%2F+%28+3%2A2+%29+
+3%2A19%2A20+=+1140+
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P( at least 2 girls ) = +1++-+748+%2F+1140+
+1+-+.6561+=+.3439+
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