SOLUTION: There are 4 freshman, 6 sophomores, 7 juniors, and 3 seniors on a school field trip. Three students are needed to carry water bottle cases. How many different ways can these studen

Algebra ->  Permutations -> SOLUTION: There are 4 freshman, 6 sophomores, 7 juniors, and 3 seniors on a school field trip. Three students are needed to carry water bottle cases. How many different ways can these studen      Log On


   

Question 1116311: There are 4 freshman, 6 sophomores, 7 juniors, and 3 seniors on a school field trip. Three students are needed to carry water bottle cases. How many different ways can these students be selected?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
In all, there are 4 + 6 + 7 + 3 = 20 students.


By selecting randomly 3 students of 20, you can do it in  C%5B20%5D%5E3 = %2820%2A19%2A18%29%2F%281%2A2%2A3%29 = 1140 ways.

In order to solve freely such problems, you need to know about Combinations.

On Combinations,  see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.