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

Question

A boy has $3$ library tickets and 8 books of his interest in the library.Of these $8$,he doesn't want to borrow Chemistry part $2$ unless Chemistry part $1$ is also borrowed.In how many ways can he choose $3$ books to be borrowed?

I did this question by taking cases
1)Both chemistry books aren't borrowed
2)Chemistry $1$ is borrowed

So,for first case $C(6,3)$ and

second $C(6,1)$ because he will be left with only one choice.

But it's answer is $C(7,2)+C(6,3)$

Answer 1

Problem is in interpretation of second case

I think problem caused here is due to misinterpretation of this statement "he doesn't want to borrow Chemistry part $2$ unless Chemistry part $1$ is also borrowed".
This statement implies that he can borrow Chemistry $2$ only when he had borrowed Chemistry $1$.But,he is not strictly bounded to borrow Chemistry part $2$ with $1$.He can borrow any two books from 7 books."Statement in your textbook states that he "can" but you had interrupted as he have to buy both books together . OR

$C(7,2)+C(6,3)$