Question

Answer the following:

A student finds 7 books of his interest but can borrow only three books. He wants to borrow the Chemistry part-II book only if Chemistry Part-I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.

Answer 1

There are 7 books of interest and only 3 books can be borrowed.

(i) If Chemistry part-I is selected, then Chemistry part-II is also borrowed. Thus the only a third book is selected from the remaining (7 – 2) = 5 books.

∴ the number of ways of selecting 3 books such that Chemistry part-I is selected

= ⁵C₁

= 5

(ii) If Chemistry part-I is not selected, then Chemistry part-II is not borrowed, therefore, he has to select all 3 books from the remaining (7 – 2) = 5 books.

∴ the number of ways of selecting 3 books such that Chemistry part-I is not selected

= ⁵C₃

= `(5!)/(3!2!)`

= `(5 xx 4)/(1 xx 2)`

= 10

Hence, the total number of ways of selecting 3 books to be borrowed

= 5 + 10

= 15