A committee of two persons is selected from two men and two women. What is the probability that the committee will have no man ?
The total number of persons $=2+2=4 .$ Out of these four person, two can be selected in $^{4} C _{2}$ ways.
No men in the committee of two means there will be two women in the committee.
Out of two women, two can be selected in $^{2} C _{2}=1$ way.
Therefore $P$ (no man) $=\frac{^{2} C _{2}}{^{4} C _{2}}$ $=\frac{1 \times 2 \times 1}{4 \times 3}$ $=\frac{1}{6}$
In a certain lottery $10,000$ tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket.
A basket contains $5$ apples and $7$ oranges and another basket contains $4$ apples and $8$ oranges. One fruit is picked out from each basket. Find the probability that the fruits are both apples or both oranges
The probability that two randomly selected subsets of the set $\{1,2,3,4,5\}$ have exactly two elements in their intersection, is :
If three letters can be posted to any one of the $5$ different addresses, then the probability that the three letters are posted to exactly two addresses is:
A bag contains $20$ coins. If the probability that bag contains exactly $4$ biased coin is $1/3$ and that of exactly $5$ biased coin is $2/3$,then the probability that all the biased coin are sorted out from the bag in exactly $10$ draws is