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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.
Solution
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
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