Six candidates are called for interview to fill four posts in an office. Assuming that each candidate is fit for each post. determine the number of ways in which : first and second posts can be filled.

Six candidates are called for interview to fill four posts in an office. Assuming that each candidate is fit for each post. determine the number of ways in which : first three posts can be filled.

Six candidates are called for interview to fill four posts in an office. Assuming that each candidate is fit for each post. determine the number of ways in which : all the four posts can be filled.

There are p copies each of n different books. Find the number of ways in which a nonempty selection can be made from them.

Eighteen guests have to be Seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the Seating arrangements can be made.

In an examinations there are three multiple choice questions and each questions has 4 choices. Find the number of ways in which a student can fail to get all answer correct.

In an Examination, a candidate has to pass in each of the four subjects. In how many ways can he fail ?

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is (1) 36 (2) 66 (3) 108 (4) 3

There are two urns. Urn A has 4 distinct red balls and urn B has 5 distinct blue balls. From each urn (two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is :

Five persons entered the lift cabin on the ground floor of a 8 floor house. Suppose each of them can leave the cabin independently at any floor beginning with the first. The total number of ways in which each of the five person can leave the cabin at any one of the 7 floor, is (a) 5^(7) (b) 7^(5) (c) 35 (d) 2520

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in the party, is :