Assume that the committee consists of 8 Republicans and 5 Democrats. A subcommittee of 4 is randomly selected from all subcommittees of 4 which contain at least 1 Democrat. What is the probability that the new subcommittee will contain at least 2 Democrats?

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Assume that the committee consists of 8 Republicans and 5 Democrats. A subcommittee of 4 is randomly selected from all subcommittees of 4 which contain at least 1 Democrat. What is the probability that the new subcommittee will contain at least 2 Democrats?

Mathematics
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good lord
lets see if we can figure out how many subcommittees contain at least one democrat, and i guess the best way to do it is figure out how many contain no democrats and subtract it from the total possible subcommittees
these things ar ekilling me and i have to have these done by 730 am

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number of subcommittees with not restriction is \[\dbinom{13}{4}=\frac{13\times 12\times 11\times 10}{4\times 3\times 2}=715\]
number of subcommittees that are all republicans are \[\frac{8\times 7\times 6\times 5}{4!}=70\] so i guess we have \[715-70=645\] total subcommittees that contain at least one democrat
that will be our denominator. now we have to figure out, of these 645 subcommittees with at least one democrat, how many have at least two
ok exactly one democrat number of ways would be \[\dbinom{5}{1}\dbinom{8}{3}\] aka \[5\times 56=280\]
so subtract this off from 645 to get the number that contain more than 1 democrat. you get \[645-280=365\] so our answer is \[\frac{365}{645}\]
that didnt work
you sure? i think the method is right. maybe a calculation error?
the more i think about it the more i think it is right. do you have an answer?
you are right
whew!!
im sorry not sure why it didnt work first time
ok did you try the other one i sent? is this an on line class?
no but home work is submitted online...
oh i see. have fun!

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