Twenty of the houses on a street receive cable t.v. and seven do not. A researcher studying the amount of time that people watch t.v. intends to visit five of the houses that receive cable t.v and two that do not. How many such selections of houses are there?

Question

Twenty of the houses on a street receive cable t.v. and seven do not.   A researcher studying the amount of time that people watch t.v. intends to visit five of the houses that receive cable t.v and two that do not.   How many such selections of houses are there?

anonymous · Answer

$$\dbinom{20}{5}$$ 
$$\frac{20\times 19\times 18\times 17\times 16}{5\times 4\times 3\times 2}$$

anonymous · Answer

oh no sorry

anonymous · Answer

i should read more carefully!

anonymous · Answer

that is how many ways to pick 5 out of the 20 that receive cable. then you have to multiply by 
$$\dbinom{7}{2}=\frac{7\times 6}{2}=21$$

anonymous · Answer

so "final answer" is 
$$\dbinom{20}{5}\times \dbinom{7}{2}=15504\times 21=325584$$

anonymous · Answer

r u sure?

amistre64 · Answer

would it be:
 
  27!
-----  ??
7! 20!

anonymous · Answer

idk?

anonymous · Answer

someone else got 20

amistre64 · Answer

i dont know either .... at least not 100% :)

if I read it right its asking similiar to how many ways can we arrange the letters mississippi to?

anonymous · Answer

well 20 is surely wrong!

anonymous · Answer

@sensei that is a totally different kind of question.  ok not "totally different" but certainly different. you are asking for arrangements

amistre64 · Answer

n!
--------------- maybe
n1! n2! n3! ... nk!

anonymous · Answer

i am fairly certain of my answer (not like usual)

amistre64 · Answer

oh im sure youre right on it ;)

anonymous · Answer

we think its to big of a selection

anonymous · Answer

counting principle says if there are n ways to do one thing and m ways to do another, then there are 
$$m\times n$$ ways to do them both. here there are clearly 
$$\dbinom{20}{5}$$ ways to choose 5 houses from a set of 20

amistre64 · Answer

would my attempt be part of it; im thinking like the "total" part of the probability

anonymous · Answer

that is the definition of 
$$\dbinom{20}{5}$$ and likewise there are 
$$\dbinom{7}{2}$$ ways of selecting 2 from a set of 7

amistre64 · Answer

then 5/total + 5/total ....  cant seem to focus on it that well

anonymous · Answer

this is not a probability question.  they are not asking for "what is the probability that mr. jones house is selected".  the question is just "how many"

amistre64 · Answer

ack!! .... yep

anonymous · Answer

soooo whats the answer?