(C) Total number of balls $= 3 + 7 + 4 = 14$.Number of ways to draw $3$ balls from $14$ is $^{14}C_3 = \frac{14 \times 13 \times 12}{3 \times 2 \times

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(C) Total number of balls $= 3 + 7 + 4 = 14$.Number of ways to draw $3$ balls from $14$ is $^{14}C_3 = \frac{14 \times 13 \times 12}{3 \times 2 \times 1} = 364$.Number of ways to draw $3$ balls of the same colour:- All $3$ red: $^3C_3 = 1$- All $3$ white: $^7C_3 = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$- All $3$ black: $^4C_3 = 4$Total favorable outcomes $= 1 + 35 + 4 = 40$.Required probability $= \frac{40}{364} = \frac{10}{91}$.

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

Medium

$A$ bag contains $3$ red,$7$ white and $4$ black balls. If three balls are drawn from the bag,then the probability that all of them are of the same colour is

A
$\frac{6}{71}$
B
$\frac{7}{81}$
C
$\frac{10}{91}$
D
None of these

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Advanced Use of permutations and combinations in probability

If $A_1, A_2, \ldots, A_{15}$ are the events of a random experiment,then which one of the following is true?

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Consider the set of all $7$-digit numbers formed by the digits $0, 1, 2, 3, 4, 5, 6$,each chosen exactly once. If a number is randomly drawn from this set,the probability that it is divisible by $4$ is

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In a box,there are $2$ red,$3$ black,and $4$ white balls. If $3$ balls are drawn together,what is the probability that they are of the same color?

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$A$ committee has to be made of $5$ members from $6$ men and $4$ women. The probability that at least one woman is present in the committee is:

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$A$ bag contains $3$ red,$7$ white and $4$ black balls. If three balls are drawn from the bag,then the probability that all of them are of the same colour is

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