Question

There are $20$ books on Albegra and Calculus in one library. For the greatest number of selections each of which consists of $5$ books on each topic possible number of Algebra books are $N$ then the value of $N/2$ is.

Answer 1

Let there be $x$ books of algebra, so there will be $20-x$ books of calculus.

Choosing $5$ of each $={}^x{C}_5\times {}^{20-x}{C}_5$

WKT for ${}^n{C}_r\times {}^{N-n}{C}_r$ is maximum

$\Rightarrow$ When $n=\frac{N}{2}$

$\Rightarrow x=\frac{20}{2}$

$=10.$

Hence, the answer is $10.$