A committee of two is to be chosen at random from a group of 7 students consisting of 4 boys and 3 girls. What is the probability that a committee of two boys will be chosen?
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Answer:
No. of ways at least one girl=Total-(none of the selected members is a girl)
=
12
C
4
−
8
C
4
=
4×3×2×1
12×11×10×9
−
4×3×2×1
8×7×6×5
=495−70=425
No. of ways of selecting exactly 2 girls=
8
C
2
+
4
C
2
=
2
8×7
×
2
4×3
=168
Probability=
425
168
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