AMC10 2018 A

AMC10 2018 A · Q4

AMC10 2018 A · Q4. It mainly tests Basic counting (rules of product/sum), Permutations.

How many ways can a student schedule 3 mathematics courses—algebra, geometry, and number theory—in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)

学生如何在 6 节课的一天中安排 3 门数学课程——代数、几何和数论，如果不能在连续的课节上修读两门数学课程？（其他 3 节课修读什么课程无关紧要。）

(A) 3 3

(B) 6 6

(D) 18 18

(E) 24 24

Answer

Correct choice: (E)

正确答案：（E）

Solution

There are 4 choices for the periods in which the mathematics courses can be taken: periods 1, 3, 5; periods 1, 3, 6; periods 1, 4, 6; and periods 2, 4, 6. Each choice of periods allows 3! = 6 ways to order the 3 mathematics courses. Therefore there are 4 · 6 = 24 ways of arranging a schedule.

数学课程可以安排的课节有 4 种选择：1、3、5 节；1、3、6 节；1、4、6 节；以及 2、4、6 节。每种课节选择允许 3! = 6 种方式安排 3 门数学课程。因此共有 4 x 6 = 24 种安排日程的方式。

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