Final answer:
Marie can select her outfit in 144 different ways.
Step-by-step explanation:
In this question, Marie has 4 new dresses and 3 shoes in her closet that she can pair together in various ways. Since any shoe can be paired with any dress, she has 4 choices for the first dress and 3 choices for the first shoe. For the second dress, she has 3 choices left, and for the second shoe, she has 2 choices left. Finally, for the third dress, she has 2 choices left, and for the third shoe, she has 1 choice left. By multiplying all the choices together, we can find the total number of ways Marie can select her outfit.
Therefore, the number of ways Marie can select her outfit is 4 * 3 * 3 * 2 * 2 * 1 = 144.