## anonymous 4 years ago 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?

1. anonymous

good lord

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

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 $\frac{365}{645}$

9. anonymous

that didnt work

10. anonymous

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

11. anonymous

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

12. anonymous

you are right

13. anonymous

whew!!

14. anonymous

im sorry not sure why it didnt work first time

15. anonymous

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

16. anonymous

no but home work is submitted online...

17. anonymous

oh i see. have fun!