really confusing, please help! a committee will consist of 3 teachers/3 students chosen from the 24 teachers & 145 students available. half of the teachers and 99 students are women. find the probability that the committee has only female members?

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really confusing, please help! a committee will consist of 3 teachers/3 students chosen from the 24 teachers & 145 students available. half of the teachers and 99 students are women. find the probability that the committee has only female members?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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(12C3/24C3)+(99C3/145C3)
why plus?
sorry i think that will be *

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so (12C2)(99C3)/((24C3)*(145C3))
here two conditions have to be satisfied simultaneously *. 12C3 not 12C2
smoochum, i got 115 for the solution for that other problem about multiples of 3
:O from the work we did??
@ dipankarstudy i think your first answer (12C3/24C3)+(99C3/145C3) is right , it's + not *
can you explain why is a + and not *
because the committee consists of 3 teachers OR 3 students it can't consist of both students and teachers it can only consist of 3 teachers, or it consists only of 3 students you use * if the committee consists of 3 teachers AND 3 students
oh it says 3 teachers and 3 students
both the teachers and students so *
no, it says 3 teachers/3 students , doesnt that mean 3 students OR 3 teachers?
how would you do only 1 teacher and only 1 student who are women then? adding?
oh i just simplified it dindatc XD sorry for the confusion
(12C3/24C3)+(99C3/145C3) 12C3 means 3 females are picked from 12 female teachers 99C3 means 3 females are picked from 99 female students
how about 1 teacher and 1 student?
my attempt for that one is: 12C1*12C2/24C3 * 99C1*46C2/145C3
Ways of choosing only females = (12C3 x 99C3) = 34 506 780 the ways of picking 3 teachers and 3 students with no restriction = (24C3) x (145C3)
answer to first question = [34 506 780 ] /[ 24C3 x 145C3 ] = 0.03426....

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