A class has 10 boys (including Doug) and 8 girls (including Cathy).
If 3 students are chosen at random to be studyhall monitors, what is the probability that Doug is selected but Cathy is not?
We are given that, the class has 10 boys and 8 girls.
Following are the combinations for 3 students selected to include Doug and not Cathy
3 boys = 10C3
2 boys, 1 girl = 10C2 * 7C1 (Since Cathy is not selected)
1 boy, 2 girls = 10C1 * 7C2 (Since Cathy is not selected)
0 boys, 3 girls = 7C3
Probability that 3 students selected include Dough but not Cathy =
=
Probability that Doug is selected but Cathy is not is 0.833
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