(D) Total number of balls $= 5 + 3 + 4 = 12$. Number of ways to draw $3$ balls from $12$ is ${}^{12}C_3 = \frac{12 \times 11 \times 10}{3 \times 2 \ti

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(D) Total number of balls $= 5 + 3 + 4 = 12$. Number of ways to draw $3$ balls from $12$ is ${}^{12}C_3 = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220$. Number of ways to draw $3$ balls of the same colour: - $3$ red balls: ${}^{5}C_3 = 10$ - $3$ black balls: ${}^{3}C_3 = 1$ - $3$ white balls: ${}^{4}C_3 = 4$ Total ways for same colour $= 10 + 1 + 4 = 15$. Probability of same colour $= \frac{15}{220} = \frac{3}{44}$. Probability of not same colour $= 1 - \frac{3}{44} = \frac{41}{44}$.

Class 11 Mathematics Probability Advanced Use of permutations and combinations in probability

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$A$ bag contains $5$ red balls, $3$ black balls, and $4$ white balls. Three balls are drawn at random. The probability that they are not of the same colour is

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A
$\frac{37}{44}$
B
$\frac{31}{44}$
C
$\frac{21}{44}$
D
$\frac{41}{44}$

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Advanced Use of permutations and combinations in probability

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