Discrete Mathematics Given 8 Perl books 17 Python books 6 Ja

Discrete Mathematics

Given 8 Perl books, 17 Python books, 6 Java books, 12 Haskell books, and 20 C++ books, how many ofthese books must we select to ensure that we have 10 books all dealing with the same programminglanguage?

Solution

It can be possible to have 10 books of either perl or java since there are only 8 books of perl and 6 books of java available in the library

10 books all dealing with the same subject = 8 + 6 + 9 + 9 + 9 + 1 = 42 books

Now how we arrived at the answer, let us suppose your first select book is perl, then you went on selecting perl books to make the total of 8, now you select java books and went on selecting the 6 java books (till now you don\'t have any language 10 books)

Now you pick 9 python books, 9 haskell books and 9 C++ books

Now the next book which you pick will be either from python, haskell or C++ which will make the count of atleast 10 books of same language

Hence the final answer is summing all the books required

=> (8 + 6 + 9 + 9 + 9 + 1) = 42

1 represents the any book which you can select to make a total of 10 books of 1 language