Question

A boy has $3$ Library tickets and $8$ books of his interest in the library. Out of these $8$, he does not want to borrow Chemistry part $II$, unless Chemistry part $I$ is also borrowed. The number of ways in which he can choose the three books to be borrowed is

Answer 1

The following are the different possibilities in which three books acn be borrowed;

(i) When Chemistry part $II$ is selected, the Chemistry part $I$ is also borrowed and the third book is selected from the remaining $6$ books.

(ii) When Chemistry part $II$ is not selected, in this case he has to select the three books from the remaining $7$ books.

First choice can be made in ${}^6{C}_1=6$ ways.

Second choice can be made in ${}^7{C}_3=\frac{7\times 6\times 5}{1\times 2\times 3}=35$ ways.

Total number of ways in which he can choose the three books to be borrowed $=6+35=41$