Question

1. The local scifi club has 100 members. At a meeting, a public vote shows that 43 members are fans of Arthur C. Clarke and 41 members are fans of Robert A. Heinlein. The random selection of a board of directors of at least how many members will guarantee that there are at least 5 Clarke fans, and also at least 5 Heinlein fans among the directors?

If n is the right answer, you must not only explain why the random selection of n members suffices, but also why selecting fewer than n members may not suffice.

Answer 1

To guarantee there are at least 5 Clarke fans, number of members to be selected = Number of non Clarke fans + 5

= (100 - 43)+5

= 62

If 61 are selected, it can have 57 non Clarke fans and 4 Clarke fans. So, minimum number to be selected to guarantee 5 Clarke fans = 62

Number of no Heinlen fans = 100-41 = 59

Number of members to be selected to guarantee at least 5 Heinlen fans = 59 + 5 = 64

If 63 are selected, it can be 59 non Heinlen fans and 4 Heinlen fans.