(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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Probability

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Advanced Use of permutations and combinations in probability

From the first $100$ natural numbers, two numbers $a$ and $b$ are selected randomly without replacement. If the probability that $a-b \ge 10$ is $\frac{m}{n}$, with $\gcd(m, n)=1$, then $m+n$ is equal to:

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Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains at least $3$ Kings.

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If four persons are chosen at random from a group of $3$ men,$2$ women and $4$ children,then the probability that exactly two of them are children is:

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If three distinct numbers are chosen randomly from the first $100$ natural numbers,then the probability that all three of them are divisible by both $2$ and $3$ is

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If the letters of the word $SUCCESS$ are rearranged,what is the probability that all identical letters come together (in $/35$)?

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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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From the first $100$ natural numbers, two numbers $a$ and $b$ are selected randomly without replacement. If the probability that $a-b \ge 10$ is $\frac{m}{n}$, with $\gcd(m, n)=1$, then $m+n$ is equal to:

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