(A) Total number of students $= 12 + 18 = 30$. Number of ways to choose $2$ students out of $30$ is given by $^{30}C_2 = \frac{30 \times 29}{2 \times

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(A) Total number of students $= 12 + 18 = 30$. Number of ways to choose $2$ students out of $30$ is given by $^{30}C_2 = \frac{30 \times 29}{2 \times 1} = 435$. Number of ways to choose $2$ girls out of $12$ is given by $^{12}C_2 = \frac{12 \times 11}{2 \times 1} = 66$. Required probability $= \frac{^{12}C_2}{^{30}C_2} = \frac{66}{435} = \frac{22}{145}$.

Class 11 Mathematics Probability Permutation and Combination based Probability

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From a class of $12$ girls and $18$ boys,two students are chosen randomly. What is the probability that both of them are girls?

A
$\frac{22}{145}$
B
$\frac{13}{15}$
C
$\frac{1}{18}$
D
None of these

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Permutation and Combination based Probability

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$A$ bag contains $4$ red, $3$ white, and $5$ blue balls. Three balls are drawn at a time randomly from the bag. Match the items from List-$I$ with those of List-$II$.
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$B$. Probability of getting $2$ white and $1$ blue ball $(ii)$ $\frac{21}{55}$
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$D$. Probability that none of the balls is white $(iv)$ $\frac{3}{11}$
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List-$I$	List-$II$
$A$. Probability of getting $1$ red, $1$ white and $1$ blue ball	$(i)$ $\frac{3}{44}$
$B$. Probability of getting $2$ white and $1$ blue ball	$(ii)$ $\frac{21}{55}$
$C$. Probability of getting $2$ red and $1$ white ball	$(iii)$ $\frac{38}{55}$
$D$. Probability that none of the balls is white	$(iv)$ $\frac{3}{11}$
	$(v)$ $\frac{9}{110}$

From a class of $12$ girls and $18$ boys,two students are chosen randomly. What is the probability that both of them are girls?

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$A$ box contains $5$ blue and $4$ white chalks. If two chalks are chosen at random,what is the probability that both chalks are of the same color?

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