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

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(A) Total number of balls $= 3 + 4 + 5 = 12$. Number of ways to select $3$ balls out of $12$ is $^{12}C_3 = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220$. For the balls to be of different colors,we must select $1$ red,$1$ white,and $1$ black ball. Number of favorable outcomes $= ^3C_1 \times ^4C_1 \times ^5C_1 = 3 \times 4 \times 5 = 60$. Probability $= \frac{60}{220} = \frac{6}{22} = \frac{3}{11}$.

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

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$A$ bag contains $3$ red,$4$ white,and $5$ black balls. If three balls are drawn at random,what is the probability that they are of different colors?

A
$3/11$
B
$2/11$
C
$8/11$
D
None of these

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Advanced Use of permutations and combinations in probability

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$A$ bag contains $3$ red,$4$ white,and $5$ black balls. If three balls are drawn at random,what is the probability that they are of different colors?

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