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प्रश्न
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that all are blue?
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उत्तर
Out of 60 marbles, five marbles can be drawn in 60C5 ways.
∴ Total number of elementary events = 60C5
Out of 20 blue marbles, five blue marbles can be chosen in 20C5 ways.
∴ Favourable number of events = 20C5 ways
Hence, the required probability is given by
\[\frac{^{20}{}{C}_5}{^{60}{}{C}_5} = \frac{20 \times 19 \times 18 \times 17 \times 16}{60 \times 59 \times 58 \times 57 \times 56}\]
\[ = \frac{19 \times 6 \times 17}{59 \times 29 \times 57 \times 7}\]
\[ = \frac{2 \times 17}{59 \times 29 \times 7}\]
\[ = \frac{34}{11977}\]
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