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Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Answer & Solution
Correct Answer:
Option
D
P(at least one graduate) = 1 - P(no graduates)
$$\eqalign{ & = 1 - \frac{{{}^6{C_3}}}{{{}^{10}{C_3}}} \cr & = 1 - \frac{{6 \times 5 \times 4}}{{10 \times 9 \times 8}} \cr & = \frac{5}{6} \cr} $$
$$\eqalign{ & = 1 - \frac{{{}^6{C_3}}}{{{}^{10}{C_3}}} \cr & = 1 - \frac{{6 \times 5 \times 4}}{{10 \times 9 \times 8}} \cr & = \frac{5}{6} \cr} $$
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