Question

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 unless Mathematics is also borrowed. In how many ways can he choose the three books to be borrowed?

• A. $40$
• B. $45$
• C. $42$
• D. $41$

Answer 1

Answer: (D)

$41$

Answer 2

Let us make the following cases : Boy borrows Mathematics Part II, then he borrows Mathematics Part I also. So, the number of possible choices is $^{6}C_{1} = 6$. Boy does not borrow Mathematics Part II, then the number of possible choices is $^{7}C_{3} = 35$. Hence, the total number of possible choices is $= 35 + 6 = 41$.