There are $3$ men and $2$ women in a Grampanchayat. A committee of two is formed. Find the probability of Q is the event that committee should contain one man and one woman.

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Solution

$\begin{matrix} 3 m e n a n d 2 w o m e n c o m m i t t e e o f t w o f o r m e d w i t h 1 m a n a n d 1 w o m a n i s =^{3} C_{1} \times^{2} C_{1} = 3 \times 2 = 6 t w o c o m m i t t e e i s f o r m e d \Rightarrow (e i t h e r 0 m a n o u t o f 3) \times (2 w o m e n o u t o f 2 w o m e n) =^{3} C_{0} \times^{2} C_{2} = 1 \Rightarrow (1 m a n o u t o f 3) \times (1 w o m e n o u t o f 2 w o m e n) =^{3} C_{1} \times^{2} C_{1} = 3 \times 2 = 6 \Rightarrow (2 m a n o u t o f 3) \times (0 w o m e n o u t o f 2 w o m e n) =^{3} C_{2} \times^{2} C_{0} = 3 \times 1 = 3 T h e n p r o b a b i l i t y o f g r a m p a n c h a y a t w i t h t w o c o m m i t t e e = \frac{(^{3} C_{1} \times^{2} C_{1})}{10} = \frac{3 \times 2}{10} = \frac{3}{5} \end{matrix}$

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There are 3 men and 2 women in a Grampanchayat. A committee of two is formed. Find the probability of Q is the event that committee should contain one man and one woman.

There are $3$ men and $2$ women in a Grampanchayat. A committee of two is formed. Find the probability of Q is the event that committee should contain one man and one woman.