Six X ' s have to be placed in thesquares of the figure below, such that each rowcontains atleast one X. In how many different wayscan this be done?

Six X 's have to be placed in the squares of the figure below, such that each row contains atleast one X. in how many different ways can this be done?

In how many ways can 7 cross marks X be placed in the given figure so that each row has at least one cross mark?

Five balls of different color are to be placed in three boxes of different size. Each box can hold all five. In how many different ways can we place the balls so that no box remains empty?

Six very good friends decide they will have lunch together ecery day . In how many different ways can they line up in the line ?

In each of the figures given below. Find x\ a n d\ y

Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?

Case 4 In how many ways 14 identical toys be distributed among three boys so that each one gets atleast one toy and no two boys get equal no of toys ?

Greg, Marcia, Peter, Jan, Bobby, and Cindy go to a movie and sit next to each other in six adjacent seats in the front row of the theater. If Marcia and Jan will not sit next to each other, in how many different arrangements can the six people sit?

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?

There are 3 books of Mathematics, 4 of Physics and 5 of English. How many different collections can be made such that each consists at least one book of each subject ?