3. 4/7 points | Previous Answers My Notes Ask Your Ellen must take 4 courses thi

Question

3. 4/7 points | Previous Answers My Notes Ask Your Ellen must take 4 courses this semester. She has a list of 4 math courses and 6 science courses to from which to choose (a) Initially Ellen is under the impression that she can simply take any four of the courses on the list. If this was the case, how many different ways could Ellen selt the four courses? 210 (b) Ellen's boyfriend tells her that he thinks that she must choose 2 math courses and 2 science courses to meet her degree requirements. If this is true, how many different ways can she select the four courses? 90 (c) Ellen's speaks to her advisor and finds out that her program actually only requires that at least one of her four courses be a math course. Knowing this, how many different ways can she select the four courses? 80 4. 1.55 points | Previous Answers My Notes Ask Your T A restaurant offers 4 different entrees, 5 different vegetables, and 5 different desserts. (a) If you are going to order one item from each category, how many different meals are possible? 100 (b) If you are going to order one entree, two different vegetables, and one dessert, how many different meals are possible? 400 (c) How many different meals are possible if you're going to order one entree, three different vegetables, and at most one dessert? (In other words you have the option of skipping dessert.) 1200

Explanation / Answer

3) c) Number of ways to select at least one math courses = total number of ways to select 4 courses - number of wasy to select zero math courses

                                                       = 210 - 6C4

                                                       = 210 - 15

                                                       = 195

4) b) Number of different meals with one entree, two different vegetables and one desert = 4 * 5C2 * 5 = 4 * 10 * 5 = 200

c) Number of different meals with one entree, three different vegetables and at most one desert = Number of different meals with one entree, three different vegetables and no desert + Number of different meals with one entree, three different vegetables and one desert

                                                           = 4 * 5C3 + 4 * 5C3 * 5

                                                           = 4 * 10 + 4 * 10 * 5

                                                           = 240

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.