Respuesta :
Answer:
So those scholarships can be awarded in 13*12 = 156 different ways ensuring that at least two of them go to seniors.
Step-by-step explanation:
In this problem, there are three scolarships.
The first step to solve this question is ensuring that two seniors receive their scolarships.
There are 4 seniors, and we must guarantee two scolarships to them. If senior A receives the first scolarship and senior B the second, or A receives the second and B the first, it is the same thing, so the order does not interfere with the problem. It means it is a combination problem.
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The formula for the number of possible combinations of r objects from a set of n objects is:
[tex]C(n,r) = \frac{n!}{r!(n-r)!}[/tex]
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So, for the senior scolarships, we have combinations of two(scolarships) objects from a set of four(seniors) objects: So
[tex]C(4,2) = \frac{4!}{4!(4-2)!} = 12[/tex]
There are 12 ways to ensure two of those scolarships to those seniors.
The are 13 students vying for the last scolarship(hree freshmen, five sophomores, 3 juniors and two seniors that didn't get the first two).
So those scholarships can be awarded in 13*12 = 156 different ways ensuring that at least two of them go to seniors.
