A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed ?

A question paper has two parts: Part A and Part B. each part containing ten questions. If the student has to choose 8 questions form part A and 5 questions from part B. In how many ways can he choose the questions?

John wants to go abroad by ship and return by air. He has a choice of 6 different ships to go and 4 airlines to return. In how many ways can he perform his journey ?

A mathematics paper consists of 10 questions divided into two parts I and II, each part containing 5 questions. A student is required to attempt 4 questions in all, taking at least 2 questions from each part. In how many ways can the student select the questions ?

In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions ?

In an examination, a question paper consists of 12 questions divided into parts i.e. Part I and Part II, containing 5 and 7 questions respectively. A student is required to attempt 8 questions, selecting at least 3 from each part.In how many ways can a Student select the questions ?

In an examination, Yamini has to select 4 questions from each part. There are 6, 7 and 8 questions in Part I, Part II and Part III respectively. What is the number of possible combinations in which she can choose the questions ?

Seven relatives of a man comprises four ladies and three gentlemen: his wife has also seven relatives-three of them are ladies and four gentlemen. In how many ways can they invite 3 ladies and 3 gentlemen at a dinner party so that there are three mans relatives and three wifes relatives?

There are three books of physics, four of chemistry and five of mathematics. How many different collections can be made such that each collection consists of (i) one book of each subject (ii) atleast one book of each subject. (iii) atleast one book of mathematics.

A water tank has steps inside it. A monkey is sitting on the topmost step(i.e., the first step). The water level is at the ninth step. If the number of steps moved down is represented by negative integers and the number of steps moved up by positive integers, represent his moves in part (i) and (ii) by completing the following, (a) -3+2 -..= -8 (b) 4-2+...= 8. In (a) the sum (-8) represents going down by eight steps. So, what will the sum 8 in (b) represent?