SOLUTION: At a certain high school, the Prom Committee is going to choose new members. There are 7 students from the Junior class and 6 students from the Senior class who are willing to be n

Question 1185849: At a certain high school, the Prom Committee is going to choose new members. There are 7 students from the Junior class and 6 students from the Senior class who are willing to be new members. In how many ways can 4 new members be chosen if 2 or fewer must be from the Senior class?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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At a certain high school, the Prom Committee is going to choose new members.
There are 7 students from the Junior class and 6 students from the Senior class who are willing to be new members.
In how many ways can 4 new members be chosen if 2 or fewer must be from the Senior class?
~~~~~~~~~~~~~~~~~

The solution to the problem is


    N(2 students from the SR class) + N(1 student from the SR class) + N(0 students from the SR class) = 

  =  +  +  = 15*21 + 6*35 + 1*35 = 560.


ANSWER.  In 560 different ways.

Solved.

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This problem is to use COMBINATIONS and the Fundamental Counting Principle.

See introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Fundamental counting principle problems
    - 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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