Successful companies such as Amway, Herbalife, and NuSkin employ multilevel marketing (MLM) schemes to distribute their products. In MLM, each distributor recruits several additional distributors to work at the first level. Each of these first-level distributors, in turn, recruits distributors to work at the second level. Distributors at any level continue to recruit distributors, forming additional levels. A distributor at any particular level typically makes a 5% commission on the sales of all distributors at lower levels in his or her "group."
a. Elaine is a distributor for an MLM company. Elaine recruits six distributors to work for her at the first level. Each of these distributors recruits an additional five distributors to work at the second level. How many distributors are under Elaine?
b. Refer to part a. Suppose each distributor at Elaine's second level recruits seven third-level distributors, and each of these third-level distributors recruits five level-four distributors. Now how many distributors are under Elaine? (Your answer should give you an insight into why some MLM distributors can earn $100,000 in commissions per month!)