Question

In a student government election, 6 seniors, 2 juniors, and 3 sophomores are running for election. Students elect four at-large senators. In how many ways can this be done?

Answer 1

Answer:

330 ways.

Step-by-step explanation:

4 senators of 11 people should be selected, that is a combination of the C(n,r) form, where

n = 11

r = 4

That's C(11,4)

The combinations form uses factorial numbers. This is the formula:  

$C(n,r)=\frac{n!}{(n-r)! r!}$

Substituting the variables for their respective data, we have

$C(11,4)=\frac{11!}{(11-4)! 4!}$

$C(11,4)=\frac{11.10.9.8.7!}{7! 4!}$

$C(11,4)=\frac{11.10.9.8}{4!}$

$C(11,4)=\frac{11.10.9.8}{4.3.2}$

$C(11,4)=\frac{7920}{24}$

$C(11,4)=330$

Students can elect four at-large senators of 330 ways.

Hope this helps!

Answer 2

4-0-0
2-1-1
1-2-1
1-0-3
0-1-3


Those are just the ones I can think of so about 5 ways