Mary works selling cards over the telephone. She sells two types of cards: birthday cards and holiday cards. Mary makes $2 for each pack of birthday cards she sells and $2.50 for each pack of holiday cards she sells. She
can work no more than 10 hours per week and it takes her an average of 15 minutes to sell one pack of birthday
and an average of 20 minutes to sell one pack of holiday cards. If she can sell no more than 35 packs of cards,
how many packs of each type of card should she sell to make the most money?

The resumâ´es of two male applicants for a college teaching position in chemistry are placed in the same file as the resumâ´es of two female applicants. two positions become available, and the first, at the rank of assistant professor, is filled by selecting one of the four applicants at random. the second position, at the rank of instructor, is then filled by selecting at random one of the remaining three applicants. using the notation m2f1, for example, to denote the simple event that the first position is filled by the second male applicant and the second position is then filled by the first female applicant, (a) list the elements of a sample space s; (b) list the elements of s corresponding to event a that the position of assistant professor is filled by a male applicant; (c) list the elements of s corresponding to event b that exactly one of the two positions is filled by a male applicant; (d) list the elements of s corresponding to event c that neither position is filled by a male applicant; (e) list the elements of s corresponding to the event a â© b; (f) list the elements of s corresponding to the event a âş c; (g) construct a venn diagram to illustrate the intersections and unions of the events a, b, and c.