# A bag contains 9 identical balls, of which are 4 are blue and 6 are green. Three balls are taken out randomly from the bag after one another. Find the probability that all three balls are blue?

Category: QuestionsA bag contains 9 identical balls, of which are 4 are blue and 6 are green. Three balls are taken out randomly from the bag after one another. Find the probability that all three balls are blue?
Editor">Editor Staff asked 11 months ago

A bag contains 9 identical balls, of which are 4 are blue and 6 are green. Three balls are taken out randomly from the bag after one another. Find the probability that all three balls are blue?

(a) \frac {5}{8}

(b) \frac {6}{19}

(c) \frac {5}{21}

(d) \frac {4}{7}

The question was posed to me in examination.

I would like to ask this question from Multiplication Theorem on Probability in chapter Probability of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options
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Editor">Editor Staff answered 11 months ago

Right choice is (c)
5
21

For explanation I would say: Since  6 balls are green, the probability of first ball to be drawn is green =
6
9

The probability of the first ball to be green, 8 balls are left and 5 out of them are green =
5
8

If the first two balls are green, then the probability of the third ball to be green =
4
7

According to multiplication theorem,
6
9
.
5
8
.
4
7
=
5
21