A bag contains 6 white, 7 red and 5 black balls. If 3 balls are drawn from bag at random, then proba

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14.Probability

easy

A bag contains $6$ white, $7$ red and $5$ black balls. If $3$ balls are drawn from the bag at random, then the probability that all of them are white is

A

$\frac{{20}}{{204}}$

B

$\frac{5}{{204}}$

C

$\frac{1}{3}$

D

None of these

Solution

(b) $3$ ball can be drawn in ${}^{18}{C_3}$ ways

Favourable cases $ = {}^6{C_3}$

$\therefore $ Required probability $ = \frac{{{}^6{C_3}}}{{{}^{18}{C_3}}} $

$= \frac{{6 \times 5 \times 4}}{{18 \times 17 \times 16}} = \frac{5}{{204}}$.

Standard 11

Mathematics

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(JEE MAIN-2022)