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Probability- People

In how many different ways can you select 4 freshmen, 5 sophomores, 3 juniors, and 7 seniors from a group containing 15 students of each standing?

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Maurizio T. | Statistics Ph.D and CFA charterholder with a true passion to teach.Statistics Ph.D and CFA charterholder wi...
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You have 15 freshmen, 15 sophomores, 15 juniors, and 15 seniors available.
We assume that the order in which the students are chosen within each "standing" is irrelevant, i.e., we only care about who they are and not the position they were picked.
 
So, there are 15C4 ways (combinations) to choose the 4 freshmen, where 15C4 is the number of possible ways to choose 4 freshmen students out of a total of 15.  Recall that 15C4 = 15!/[4!(15-4)!]=1365.
Similarly, you have 15C5 different ways to choose the 5 sophomores, 15C3 to choose the juniors, and 15C7 different ways to choose the seniors.
 
Now, multiply these numbers and you have the total number of different ways to perform the task that was assigned.
 
 
Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
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You pick 4 out 15, 5 out of 15, 3 out of 15, and 7 out of 15. Since all these events are independent, you can use multiplication principle to get the answer.
 
Answer: (15C4)(15C5)(15C3)(15C7)
Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
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The number of ways of choosing k objects from a set of n objects is given by the binomial coefficient
 
(n k) = n!/k!/(n-k)!
 
Therefore, there are
 
(15 4) =15!/4!/9! = 1365
 
ways to choose 4 freshmen from a group of 15 freshmen.
 
There are
 
(15 4)*(15 5)*(15 3)*(15 7)=1365*3003*455*6435
 
ways to select 4 freshmen, 5 sophomores, 3 juniors, and 7 seniors from a group containing 15 students of each standing.