8freshmen, 9 sophomores, 9 juniors, and 7 seniors are eligible to be on a committee.
in how many ways can a dance committee be chosen if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors.

answer: 17,082

step-by-step explanation:

you need to multiply the amount of possibilities and then subtract one each time (because one person has been chosen).

the equation is (8*7*6*5)+(9*8*7*6*5)+(9*8)+(7*6*5)

each parenthesis' units correspond to the number of people that can be elected. message me if that doesn't make sense and i can explain it better.

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.