Question

Suppose you choose four booksto read from a summer readinglist of 12 books. How manydifferent combinations of booksare possible?noNote: nCr =n!r!(n-r)!nEnter

Answer 1

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Explanation:

Total number of books = 12

n = 12

amount to be chosen = 4

r = 4

To determine the different combination of books possible, we will use the combination formula:

$^nC_r\text{ = }\frac{n!}{r!(n\text{ - r)!}}$

substitute the values:

$\begin{gathered} ^{12}C_4\text{ = }\frac{12!}{4!(12\text{ - 4)!}} \\ ^{12}C_4\text{ = }\frac{12!}{4!8\text{!}} \\ =\text{ }\frac{12\times11\times10\times9\times8!}{4!\times8\text{!}} \\ =\text{ }\frac{12\times11\times10\times9}{4!}\text{ } \\ =\text{ }\frac{12\times11\times10\times9}{4\times3\times2\times1}\text{ } \\ \\ ^{12}C_4\text{ }=\text{ }495 \end{gathered}$

495 different combination of books is possible