SOMEONE PLEASE HELP ME ASAP, PLEASE!!There are 24 students in Mrs. Noether's third grade class, and there are 3 books on the reading list for book reports this quarter. Mrs. Noether wants to assign 8 students to Book A, 10 students to Book B, and 6 students to Book C. How many distinct ways can she do this?This is a combination problem with grouping.
Accepted Solution
A:
Answer:The number of distinct ways she can do this is: 6635520 waysStep-by-step explanation:If we have to chose r items out of a total of n items then the number of ways of doing so is given by:[tex]n_C_r=\dfrac{n!}{r!\times (n-r)!}[/tex]There are 24 students in Mrs. Noether's third grade class.Now, Mrs. Noether wants to assign 8 students to Book A.This means that the number of ways of doing so is:[tex]{24}_C_{8}[/tex]10 students are to be assigned to Book B.The number of ways of doing so is: [tex]{24}_C_{10}[/tex]and 6 students to Book C.The number of ways of doing so is: [tex]{24}_C_{6}[/tex]Hence, the total number of distinct ways of doing so is:[tex]{24}_C_{8}\times {24}_C_{10}\times {24}_C_{6}[/tex]which on solving gives: 6635520 ways