Math Problem Statement
安排包含x和y在內的12個人分坐成兩行,每行有6個人。若x和y須相鄰而坐,求安排坐位的方法數目
Solution
要解決這個問題，我們可以將整個排列問題分成幾個步驟來處理。
步驟 1: 把 x 和 y 看作一個單位
由於 x 和 y 必須相鄰而坐，我們可以將他們看作一個單位。這樣，我們實際上只需要安排 11 個單位（其中一個單位是 x 和 y，其他是其餘 10 個人）。
步驟 2: 安排 11 個單位的排列方式
現在要將這 11 個單位排列在兩行，每行有 6 個位置。這是一個典型的排列組合問題。我們首先從 12 個座位中選出 6 個來放置這 11 個單位。選擇的
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Permutation
Combination
Adjacency in Seating Arrangements
Formulas
n! (Factorial for Permutation)
C(n, k) (Combination formula for selecting k items from n)
Permutation of distinct units: P(n, r) = n! / (n - r)!
Theorems
Fundamental Principle of Counting
Suitable Grade Level
Grades 9-12
Related Recommendation
Arrangement of 12 People in Two Rows with x and y Adjacent
How to Seat 6 People in 11 Seats with 3 People Sitting Together
Arrange 5 Men, 4 Women, and 3 Children with Men Sitting Together
Permutations with Distance Constraint: Arranging 12 People with Restrictions
Arranging 5 Men, 4 Women, and 3 Children with Men Sitting Together