# A Bag Contains 8 Red, 3 White and 9 Blue Balls. If Three Balls Are Drawn at Random, Determine the Probability that All the Three Balls Are Blue Balls - Mathematics

A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that all the three balls are blue balls

#### Solution

Out of  20 balls, three balls can be drawn in 20C3 ways.
∴ Total number of elementary events = 20C3

Out of nine blue balls, three blue balls can be chosen in 9C3 ways.
∴ Favourable number of events = 9C3 ways.
Hence, required probability = $\frac{^{9}{}{C}_3}{^{20}{}{C}_3} = \frac{9 \times 8 \times 7}{20 \times 19 \times 18} = \frac{7}{95}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 29.1 | Page 47