A shelf contains 20 books of which 4 are single volume and the other form sets of 8, 5, and 3 volumes. Find the number of ways in which the books may be arranged on the shelf so that volumes of each set will not be separated. (ii)volumes of each set remain in their due order.

There are 3 copies each of 4 different books. The number of ways in which they can be arranged in a shelf is

Find the number of ways in which 22 different books can be given to 5 students, so that two students get 5 books each and all the remaining students get 4 books each.

There are six periods in each working day of a school. Find the number of ways in which 5 subjects can be arranged if each subject is allowed at least one period and no period remains vacant.

There are 2 identical white balls, 3 identical red balls, and 4 green balls of different shades. Find the number of ways in which they can be arranged in a row so that at least one ball is separated from the balls of the same color.

There are (n + 1) white and (n + 1) black balls, each set numbered 1 to n + 1. The number of ways in which the balls can be arranged in a row so that adjacent balls are of different colours, is

The number of ways in which a committee of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee contains at least 3 ladies is

There are 5 teachers and 20 students . Out of them a committee of teachers and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees (a) a particular teacher is included ? (ii) a particular student is excluded ?

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)

Find the number of ways in which 3 distinct numbers can be selected from the set {3^(1),3^(2),3^(3),..,3^(100),3^(101)} so that they form a G.P.

A committee of 5 persons is to be formed from 7 men and 3 women. i. Find the number of ways to form the committee so that it contains 5 men. ii. Find the number of ways to form the committee so that it contains 4 men and 1 women. iii. Find the number of ways to form the committee so that it contains atleast 1 women.