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.

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

Poor Dolly’s T.V. has only 4 channels, all of them quite boring. Hence it is not surprising that she desires to switch (change) channel after every one minute. Then find the number of ways in which she can change the channels so the she is back to her original channel for the first time after 4 min.

In how many ways can a party of 6 men be selected out of 10 Hindus, 8 Muslims, and 6 Christians? If the party consists of at least one person of each religion, find the number of ways of selection. (Consider only the religion of the person).

Column I, Column II The number of five-digit numbers having the product of digit 20 is, p. > 70 A closest has five pairs of shoes. The number of ways in which four shoes can be drawn from it such that there will be no complete pair is, q. <60 Three ladies have each brought their one child for admission to a school. The principal wants to interview the six persons one by one subject to the condition that no mother is interviewed before her child. The number of ways in which interview can be arranged is, r. in (50 ,110) The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is, s. in (40 ,70)

In a certain an algebraical exercise book there and 4 examples on arithmetical progression, 5 examples on permutation and combination, and 6 examples on binomial theorem. Find the number of ways a teacher can select or his pupils at least one but not more than 2 examples from each of these sets.

Three balls marked with 1, 2 and 3 are placed in an urn. One ball is drawn, its number is noted, then the ball is returned to the urn. This process is repeated and then repeated once more. Each ball is equally likely to be drawn on each occasion. If the sum of the number noted is 6, then the probability that the ball numbered with 2 is drawn at all the three occassion, is

The number of ways to fill each of the four cells of the table with a distinct natural number such that the sum of the numbers is 10 and the sums of the numbers placed diagonally are equal is a. 4 b. 8 c. 24 d. 6

(i) Count the total number of ways of answering 6 objective type questions , each question having 4 choices. (ii) In how many ways 10 pigeons can be placed in 3 different pigeon holes ? (iii) Find the number of ways of distributing 12 distance prizes to 10 students ?