Math Problem Statement
A school dance committee is made up of 3 freshman, 2 sophomores, 5 juniors, and 3 seniors.
How many ways are there to sit the committee in a row at a meeting if the students must sit together by grade? Correct= 207360
How many ways are there to sit the committee in a row at a meeting if the freshman,sophomores, and juniors must sit by grade, but the seniors can sit wherever they want?
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Combinatorics
Factorials
Permutations
Formulas
n! (Factorial of n)
Ways to arrange groups: Total arrangement = (number of groups)! × (permutations within each group)
Theorems
Fundamental Principle of Counting
Suitable Grade Level
Grades 9-12
Related Recommendation
Combinatorics: Arranging a School Dance Committee by Grade
Combinatorics Problem: Arranging a School Dance Committee by Grade
Combinatorics: Choosing 17 Students for a Dance Committee from 8 Freshmen, 9 Sophomores, 10 Juniors, and 8 Seniors
Combinatorics Problem: Group Seating Arrangement with Restrictions
Permutations of 5 Students with Restrictions: Beth Not Standing Next to Dan