Five boy and five girls sit alternately around a round table. In how many ways can this be done?

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. a. In how many ways can this be done? b. How many of these committees would consist of 1 man and 2 women?

A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of Q at least 3 women?

A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of Q exactly 3 women

In a class there are 25 boys and 10 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a competition. In how many ways can the teacher make the selection?

In rating 20 brands of cars, a car magazine picks a first,second,third,fourth and fifth best brand and then 7 more as acceptable, In how many ways can it be done?

A committee of 6 is to be choosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done?