A committee of two persons is selected from two men and two women. What is the probability that the committee will have  one man ?

Vedclass pdf generator app on play store
Vedclass iOS app on app store

The total number of persons $=2+2=4 .$ Out of these four person, two can be selected in $^{4} C _{2}$ ways.

One man in the committee means that there is one woman. One man out of $2$ can be selected in $^{2} C _{1}$ ways and one woman out of $2$ can be selected in $^{2} C _{1}$ ways.

Together they can be selected in $^{2} C _{1} \times^{2} C _{1}$ ways.

Therefore $P$ (One man) $=\frac{^{2} C _{1} \times^{2} C _{1}}{^{4} C _{2}}$ $=\frac{2 \times 2}{2 \times 3}=\frac{2}{3}$

Similar Questions

The probability that a randomly chosen $5-digit$ number is made from exactly two digits is

  • [JEE MAIN 2020]

Four fair dice $D_1, D_2, D_3$ and $D_4$ each having six faces numbered $1,2,3,4,5$ and $6$ are rolled simultaneously. The probability that $D_4$ shows a number appearing on one of $D_1, D_2$ and $D_3$ is

  • [IIT 2012]

A bag contains $5$ distinct Red, $4$ distinct Green and $3$ distinct Black balls. Balls are drawn one by one without replacement,then the probability of getting a particular red ball in fourth draw is-

The number lock of a suitcase has $4$ wheels, each labelled with ten digits i.e., from $0$ to $9 .$ The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

From a group of $7$ men and $4$ ladies a committee of $6$ persons is formed, then the probability that the committee contains $2$ ladies is