11. You have a textbook for each of the following subjects: Spanish, English, Chemistry, Geometry, History, and Psychology. If you choose 4 of these books at random to arrange on a shelf, what is the probability that the Geometry textbook will be first from the left and the Chemistry textbook will be second from the left? The number of possible outcomes in the sample space is the number of permutations of the 6 books' order, or 6 ! The number of favorable out comes is the number of permutations of the 4 remaining books order. \( \begin{array}{l} P(\text { Geometry } 1 \text { st, Chemistry } 2 \mathrm{nd})=\frac{4!}{6!} \\ =\frac{4!5)}{6(5)(4!)} \quad \text { Expand } 6!\text { and divide out common factors. } \\ =\frac{1}{30} \text { Simplify. }\end{array} \)

Did you know that probability theory, which forms the backbone of your calculations, dates back to the 16th century? Mathematicians like Gerolamo Cardano and later Blaise Pascal laid the groundwork while trying to solve gambling problems. They were the pioneers who transformed mere guesses into calculated risks, paving the way for the mathematical foundations we rely on today! Now, let's make sense of this in real life! Imagine you're organizing a bookshelf for a tutoring center and need to display the Geometry and Chemistry books prominently to catch attention. By applying probability to choose and arrange these books, you can not only create an appealing layout but also strategically highlight the subjects in demand. It's a perfect example of how probability can guide everyday decision-making!