(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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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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