Question

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?

Answer 1

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

\[\frac{^{20}{}{C}_5}{^{60}{}{C}_5} = \frac{20 \times 19 \times 18 \times 17 \times 16}{60 \times 59 \times 58 \times 57 \times 56}\]

\[ = \frac{19 \times 6 \times 17}{59 \times 29 \times 57 \times 7}\]

\[ = \frac{2 \times 17}{59 \times 29 \times 7}\]

\[ = \frac{34}{11977}\]