Seven relatives of a man comprises four ladies and three gentlemen: his wife has also seven relatives-three of them are ladies and four gentlemen. In how many ways can they invite 3 ladies and 3 gentlemen at a dinner party so that there are three mans relatives and three wifes relatives?

There are 6 gentlemen and 3 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are seated together ?

There are 6 gentlemen and 5 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are together ?

A child has four pocket and three marbles. In how many ways can the child put the marbles in its pocket?

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in the party, is :

Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated ? Find also the number of ways of their seating if all the ladies sit together.

A man has three friends. The number of ways he can invite one friend everyday for dinner on six successive nights so that no friend is invited more than three times is a. 640 b. 320 c. 420 d. 510

A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed ?

A packet of plain biscuits costs Rs 6 and that of chocolate bisuits costs Rs 9. A house-wife has Rs 72 and wants to buy at least three packets of plain biscuits and at least four of chocolate biscuits. How many of each type should she buy so that she can have maximum number of packets? Make it as a LPP and solve it graphically.