(A) Total number of ways to select $2$ persons from $13$ is $^{13}C_2 = \frac{13 \times 12}{2 \times 1} = 78$. Number of ways to select no women (i.e.

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(A) Total number of ways to select $2$ persons from $13$ is $^{13}C_2 = \frac{13 \times 12}{2 \times 1} = 78$. Number of ways to select no women (i.e.,$2$ men) is $^8C_2 = \frac{8 \times 7}{2 \times 1} = 28$. Probability of selecting no women is $P(\text{no woman}) = \frac{28}{78} = \frac{14}{39}$. Probability of selecting at least one woman is $1 - P(\text{no woman}) = 1 - \frac{14}{39} = \frac{25}{39}$.

Class 11 Mathematics Probability Permutation and Combination based Probability

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Out of $13$ applicants for a job,$5$ are women and $8$ are men. Two persons are to be selected for the job. What is the probability that at least one woman is selected?

A
$25/39$
B
$14/39$
C
$5/13$
D
$10/13$

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Permutation and Combination based Probability

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Out of $13$ applicants for a job,$5$ are women and $8$ are men. Two persons are to be selected for the job. What is the probability that at least one woman is selected?

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