Probability- People

Question

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?

Answer 1

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.

 

 

Answer 2

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.

 

Answer 3

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)