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In how many ways can a student org form a committee of 4 members from
3 freshmen, 4 sophomores, 9 juniors, and 4 seniors if each year level will be represented?
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Notice that the problem has 4 (four) levels, and it requires that each and every level
be presented in the committee of 4.
It means that from each level, exactly one representative can be and should be elected.
One representative of 3 freshmen can be elected in 3 ways.
One representative of 4 sophomores can be elected in 4 ways.
One representative of 9 juniors can be elected in 9 ways.
One representative of 4 seniors can be elected in 4 ways.
Now, guided by the Fundamental counting principle, one may conclude that
the number of all possible different committees as described in the problem
is the product 3*4*9*4 = 432. ANSWER
Solved and carefully/thoroughly explained.
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On Fundamental counting principle, see the lesson
- Fundamental counting principle problems
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 lesson is 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.