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Composite Function

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Question

There are 20 books on Algebra & Calculus in our library. The greatest number of selections each of which consists of 5 books on each topic is possible only when there are _________ books on each topic in the library.

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Solution

Lets assume there are $x$ algebra books so $(20 - x)$ calculus books are available

Number of possible ways of selecting $5$ from each is $^{x} C_{5} .^{20 - x} C_{5}$

it will be maximum when $x = 10$ since $^{10} C_{5}$ is a maximum value

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