Three are 4 men and 6 women in a city council.If one council member is selected for a committee at random how likely is it that it is women ?

Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.

Urn A contains 6 red and 4 black balls and urn B contains 4 and 6 black balls. One ball is drawn at random from urn A and B placed in urn B. Then one ball is drawn at random from urn B and placed in urn A. If one ball is now drawn at random from urn A, the porbability that it is red.

The number of ways in which we can choose a the committee from four men and six women so that the committee includes at least two men and exactly twice as many women as women as men is :

A beg contains 4 red and 4 black , another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

A committee of 6 is chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. The number of ways this can be done if two particular women refuse to serve on the same committee is

The sum of the numerator and decominator of a fraction is 24. If 4 is subtracted from the numerator and 5 from its denominator, then it reduces to 1/4 . Find the fraction. OR The women and five men can together finish an embroidary work in 4 days. While three women and 6 men can finish in 3 days. Find the time taken by one women alone and also that taken by one man alone.

In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together

A group consists of 4 girls and 7 boys .In how ways can a team of 5 members be selected ,if the team has ? (i) no girl (ii) atleast one boy and one girl ? (iii) at least three girls ?