(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

Two numbers $x$ and $y$ are chosen at random (without replacement) from the set $\{1, 2, 3, \dots, 1000\}$. The probability that $|x^4 - y^4|$ is divisible by $5$ is -

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If a coin is tossed seven times,then the probability of getting exactly three heads such that no two heads occur consecutively is

MediumTS EAMCET 2025

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$A$ container contains nine balls: three red,four blue,and two green. If three balls are selected at random from the container without replacement,what is the probability that all three balls are of different colors?

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If three numbers are drawn at random successively without replacement from a set $S = \{1, 2, \ldots, 10\}$,then the probability that the minimum of the chosen numbers is $3$ or their maximum is $7$ is:

MediumAP EAMCET 2017

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Two numbers are selected at random from $40$ consecutive natural numbers. What is the probability that the sum of the numbers is odd?

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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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Two numbers $x$ and $y$ are chosen at random (without replacement) from the set $\{1, 2, 3, \dots, 1000\}$. The probability that $|x^4 - y^4|$ is divisible by $5$ is -

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