Question

Acellus A Suppose you choose four books to read from a summer reading list of 12 books. How many different combinations of books are possible? Note: = n! r!(n-r)!

Answer 1

Answer

There are 495 different combinations.

Explanation

Picking 4 books to read out of 12 books, with the order of picking unimportant is evaluated as ¹²C₄

$\begin{gathered} ^{1}^{2}C_{4}=\frac{12!}{4!(12-4)!}=\frac{12!}{4!\times8!}=\frac{12\times11\times10\times9\times8!}{4!\times8!} \\ =\frac{12\times11\times10\times9}{4\times3\times2\times1} \\ =495 \end{gathered}$

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