Question

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?

Answer 1

good lord

Answer 2

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

Answer 3

these things ar ekilling me and i have to have these done by 730 am

Answer 4

number of subcommittees with not restriction is
\[\dbinom{13}{4}=\frac{13\times 12\times 11\times 10}{4\times 3\times 2}=715\]

Answer 5

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

Answer 6

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

Answer 7

ok exactly one democrat number of ways would be
\[\dbinom{5}{1}\dbinom{8}{3}\] aka
\[5\times 56=280\]

Answer 8

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
\[\frac{365}{645}\]

Answer 9

that didnt work

Answer 10

you sure? i think the method is right. maybe a calculation error?

Answer 11

the more i think about it the more i think it is right. do you have an answer?

Answer 12

you are right

Answer 13

whew!!

Answer 14

im sorry not sure why it didnt work first time

Answer 15

ok did you try the other one i sent? is this an on line class?

Answer 16

no but home work is submitted online...

Answer 17

oh i see. have fun!