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?

Add one square to each figure to make each figure below have a line of symmetry

In how many ways the letters of the word DIPESH can be placed in the squares of the adjoining figure so that no row remains empty?

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 ?

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover cards numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is a. 264 b. 265 c. 53 d. 67

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?

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 tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular and two on the other side. In how many ways can they be seated?

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?

Each of the six squares in the strip shown in the fig., is to be coloured with anyone of ten different colours so that no two adjacent squares have the same colour. Find the number of ways of colouring the strip.

A fair coin is tossed four times, and a person wins Re. 1 for each head and loses Rs 1.50 for each tail that turns up. From the sample space. calculate how many different amounts of money you can have after four tosses and the probability of having each of the these amounts.