In a village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme, 20 families are to be chosen for assistance, of which at least 18 families must have atmost 2 children. In how many ways can the choice be made ?

From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition, at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made ?

A family consists of a grandfather, 5 sons and daughters and 8 grand child. They are to be seated in a row for dinner. The grand children wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. In how many ways can the family be made to sit?

In a backward state, there are 729 families having six children each. If probability of survival of a girl is 1/3 anf that of a boy is 2/3 , find the number of families having 2 girls and 4 boys. Do you believe that a female child is neglected in backward areas. What steps should be taken to restore respect of a female child in society?

Sohan has x children by his first wife. Geeta has (x+1) children by her first husband. The marry and have children of their own. The whole family has 24 children. Assuming that two children of the same parents do not fight, prove that the maximum possible number of fights that can take place is 191.

A team of ten is to be formed from 6 male doctors and 10 nurses of whom 5 are male and 5 are female. In how many ways can this be done, if the team must have atleast 4 doctors and atleast 4 nurses with atleast 2 male nurses and at least 2 female nurses?

Sanya has a piece of land which is in the shape of a rhombus (See Fig. ). She wants her four children to work on the land and produce different crops to suffice the needs of their family. She divided the land in four parts by joining its opposite comers. If the perimeter of the land is 400 m and one of the diagonals is 160 m, how much area each child will get to work on.