Chapter 13 - Counting and Probability - 13.2 Permutations and Combinations - 13.2 Asses Your Understanding - Page 855: 48

$6,302,555,018,760$

Order matters here,so the situation involves permutation. We know that the number of permutations for $n$ objects taken $r$ at a time is given by the formula $P(n,r)=\dfrac{n!}{(n-r)!}.$ Here, we havhe $n=365$ and $r=5$ Hence, \begin{align*} P(365,5)&=\dfrac{365!}{(365-5)!}\\ &=\dfrac{365\cdot364\cdot363\cdot362\cdot361\cdot360!}{360!}\\ &=365\cdot364\cdot363\cdot362\cdot361\\ &=6,302,555,018,760\end{align*}