Question 2

(a) A cabinet has 8 members. In how many ways

(i) Can all 8 members line up for a photograph?

(ii) Can they choose the president, the vice president and the secretary of the club.

(iii) Can they choose five members to attend a reginal general meeting.

(b) Suppose that 60% of the student body at a large university are in favour of a ban

on drinking in hostels. Suppose five students are to be randomly sampled. Find

the probability that

(i) Two favour the ban

(ii) Less than four favour the ban

(iii) At least one favour the ban

(c) The number of industrial injuries per working week in a particular factory is known

to follow a Poisson distribution with mean 2.5. Find the probability that in a

particular week there will be:

(i) Less than 2 accidents

(ii) More than 2 accidents

(iii) In a four week period there will be no. accidents