A television repair company uses a particular spare part at a rate of four per week. (C) Assuming that requests for this spare part occur at random, find the probability that

(a) exactly six are used in a particular week,

(b) at least ten are used in a two-week period,

(c) exactly six are used in each of three consecutive weeks. The manager decides to replenish the stock of this spare part to a constant level n at the start of each week.

(d) Find the value of n such that, on average, the stock will be insufficient no more than once in a 52-week year.. (L)