A boy has 3 library tickets and 8 books of his interest in the library

1.	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?
Answer» Let us make the following cases: Case (i) Boy borrows Mathematics Part II, then he borrows Mathematics Part I also. So the number of possible choices is ⁶C₁ = 6. Case (ii) Boy does not borrow Mathematics Part II, then the number of possible choices is ⁷C₃ = 35. Hence, the total number of possible choices is 35 + 6 = 41.

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?

Answer»

Let us make the following cases:

Case (i)

Boy borrows Mathematics Part II, then he borrows Mathematics Part I also.

So the number of possible choices is ⁶C₁ = 6.

Case (ii)

Boy does not borrow Mathematics Part II, then the number of possible choices is ⁷C₃ = 35.

Hence, the total number of possible choices is 35 + 6 = 41.