## Related questions with answers

Question

State if the possible arrangements represent permutations or combinations, then state the number of possible arrangements. A student chooses at random 4 books from a reading list of 11 books.

Solution

VerifiedStep 1

1 of 2The order of the books is not important so the possible arrangements represent a $\textit{\color{#c34632}{combination}}$.

Use the combination formula:

$_n C_r=\dfrac{n!}{r!(n-r)!} \color{white}{\tag{1}}$

Substitute $n=11$ and $r=4$:

$_{11} C_4=\dfrac{11!}{4!(11-4)!}$

$_{11} C_4=\dfrac{11!}{4!7!}$

$_{11} C_4=330$

So, there are $\color{#c34632}{330\text{ arrangements}}$.

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