(D) Total number of balls $= 5 + 7 + 4 = 16$. Number of ways to draw $3$ balls out of $16$ is given by $^{16}C_3 = \frac{16 \times 15 \times 14}{3 \ti

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(D) Total number of balls $= 5 + 7 + 4 = 16$. Number of ways to draw $3$ balls out of $16$ is given by $^{16}C_3 = \frac{16 \times 15 \times 14}{3 \times 2 \times 1} = 16 \times 5 \times 7 = 560$. Number of ways to draw $3$ white balls out of $5$ is given by $^{5}C_3 = \frac{5 \times 4 \times 3}{3 \times 2 \times 1} = 10$. Required probability $= \frac{^{5}C_3}{^{16}C_3} = \frac{10}{560} = \frac{1}{56}$.

Class 11 Mathematics Probability Permutation and Combination based Probability

Easy

$A$ bag contains $5$ white,$7$ black and $4$ red balls. Three balls are drawn from the bag at random. The probability that all the three balls are white,is

A
$\frac{3}{16}$
B
$\frac{3}{5}$
C
$\frac{1}{60}$
D
$\frac{1}{56}$

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$A$ bag contains $5$ white,$7$ black and $4$ red balls. Three balls are drawn from the bag at random. The probability that all the three balls are white,is

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