SOLUTION: Fifteen students are going on their spring break. They plan to travel in three vehicles-One seating seven, one seating five, and one seating three students. In how many ways can t

Question 1110975: Fifteen students are going on their spring break. They plan to travel in three vehicles-One seating seven, one seating five, and one seating three students. In how many ways can the students group themselves for their trip?
I attempted 15!/7!5!3! =360,360

Answer by ikleyn(52835) (Show Source): You can put this solution on YOUR website!
.

1.  You can choose seven of 15 by  ways to the first, 7-seating wheel.

     = .



2.  You can choose five of remaining 15-7 = 8 by  ways to the second, 5-seating wheel.

     = .


3.  And that is all.  The remaining  15-7-5 = 3 persons are just uniquely defined, and you have nothing more to select.



4.  So, your final answer is the product of these two numbers:

     . 


5.  I leave it to you to complete these calculation.

----------------
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.

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