Eleven animals of a circus have to be placed in eleven cages (one in each cage), if 4 of the cages are too small for 6 of the animals, then find the number of the ways of caging all the animals.

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.

Let a person have 3 coins of 25 paise, 4 coins of 50 paise and 2 coins of 1 rupee. Then inhow may ways can he give none or some coins to a beggar? Further find the number of ways so that (i) he gives at least one coin of one rupee. (ii) he gives at least one coin of each kind.

There are eight rooms on the first floor of a hotel, with four rooms on each side of the corridor, symmetrical situated (that is each room is exactly opposite to one other room). Four guests have to be accommodation In four of the eight rooms (that is, one in each) such that no two guests are in adjacent rooms or in opposite rooms. If N is the number of ways in which guests can be accommodated. Then the value of N/6 is

There are eight rooms on the first floor of a hotel, with four rooms on each side of the corridor, symmetrical situated (that is each room is exactly opposite to one other room). Four guests have to be accommodation In four of the eight rooms (that is, one in each) such that no two guests are in adjacent rooms or in opposite rooms. If N is the number of ways in which guests can be accommodated. Then the value of N/6 is

Find the number of ways in which one can post 4 letters in 6 letter boxes.

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

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 person invites a group of 10 friends at dinner and sits 5 on a round table and 5 more on another round table, 4 on one round table and 6 on the other round table. Find the number of ways in each case in which he can arrange the guest.

A small metallic sphere is suspended by a light spring of force constant k from the ceilling of a cage, which is accelerating uniformly by a force F in the upward direction. The ratio of mass of the cage to that of the sphere is 'n'. Find the potential energy stored in the spring.

There are 2n guests at a dinner party. Supposing that eh master and mistress of the house have fixed seats opposite one another and that there are two specified guests who must not be placed next to one another, show that the number of ways in which the company can be placed is (2n-2)!xx(4n^2-6n+4)dot