There are 6 women and 4 men in the city council. If two council members are selected at random, then what is the probability that those two are women?

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{There} \mathrm{are} 6 \mathrm{women} \mathrm{and} 4 \mathrm{men}. \\ \Rightarrow \mathrm{Total} \mathrm{members}=6+4=10 \\ \mathrm{Now} \mathrm{two} \mathrm{council} \mathrm{members} \mathrm{are} \mathrm{selected} \mathrm{at} \mathrm{random} \\ \mathrm{Probability} \mathrm{that} \mathrm{those} \mathrm{two} \mathrm{are} \mathrm{women}=\frac{{}^6{\mathrm{C}}_2}{{}^{10}{\mathrm{C}}_2} \\ =\frac{{\displaystyle \frac{6\times 5}{2\times 1}}}{{\displaystyle \frac{10\times 9}{2\times 1}}} \\ =\frac{6\times 5}{10\times 9} \\ =\frac{\mathbf{1}}{\mathbf{3}}\mathbf{ }\left(\mathbf{Answer}\right) \end{gathered}$$

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