SOLUTION: 9 freshmen, 6 sophomores, 10 juniors, and 8 seniors are eligible to be on a committee. If a committee of 14 students is chosen at random, what is the probability that it is made up

Algebra ->  Probability-and-statistics -> SOLUTION: 9 freshmen, 6 sophomores, 10 juniors, and 8 seniors are eligible to be on a committee. If a committee of 14 students is chosen at random, what is the probability that it is made up      Log On


   



Question 1153110: 9 freshmen, 6 sophomores, 10 juniors, and 8 seniors are eligible to be on a committee. If a committee of 14 students is chosen at random, what is the probability that it is made up of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors?
Round your answer to 6 decimal places as needed.

Found 2 solutions by ikleyn, VFBundy:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

First, notice that  2+3+4+5 = 14  and  9+6+10+8 = 33.


Now use the formula  P = %28C%5B9%5D%5E2%2AC%5B6%5D%5E3%2AC%5B10%5D%5E4%2AC%5B8%5D%5E5%29%2FC%5B33%5D%5E14.


Happy calculations (!)

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In the formula, C%5Bn%5D%5Ek is the number of combinations of "n" items taken "k" at a time.

On Combinations,  see introductory 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.



Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
%289C2+%2A+6C3+%2A+10C4+%2A+8C5%29%2F%2833C14%29

=

=%2836+%2A+20+%2A+210+%2A+56%29%2F%28818809200%29

=8467200%2F818809200

= 0.010341