The cityhousing authority has recieved 50 applications from qualified applicants for eight low income?

Question

apartment. Three of the apartment are on the north side of town, and 5 are on the south aside. If the apartmnt are to be assigned by means of lottery, what is the probability that: a specfic qualified applicant will be selected for one of these apartment?
b.) Two specific qualified applicants will be selected for apartments on the same side of the town?

need help.. anyone? thanks!!! =))

Answer 1

a) Let C(n,k) be the binomial coefficient "n-choose-k", the number of ways to choose k objects from a set of n. C(n,k)=n!/[k!(n-k)!]

There are C(50,8) ways to choose the 8 applicants who are selected.

The number of combinations that involve the specific applicant is C(49,7), because the 8 selected applicants include the specific applicant and any 7 of the remaining 49.

The probability that the applicant is selected is
C(49,7)/C(50,8)=49!/[7!42!] / ( 50!/[8!42!] )
= 49!8!42! / [50!7!42!] = 8/50 = 0.16.

Not necessarily the simplest way to arrive at this, but the method used can be applied to man similar problems.

b) First find the probability that they will be selected for an apartment on the north side, and then the south side.

For the north side, there are 3 openings, so the probability is C(48,1) / C(50,3) = 48!3!47!/[1!47!50!]=2*3/(49*50).

For the south side, there are 5 openings, so the probability is
C(48,3) / C(50,5) = 48!5!45! / [ 3!45!50!]=4*5/(49*50).

Probability of either one happening is (6+20)/(49*50).