Question

A scientific laboratory needs to assign an employee to serve as safety captain for each weekday in May (including May Day and Memorial Day Monday). As it happens, this year there are 21 weekdays in May and the laboratory has 21 employees who are qualified and available to serve as safety captain on each of these days. These 21 qualified employees consist of 3 team leaders, 5 scientists, and 13 technicians. Since there are 21 days and 21 employees to chose from the laboratory will randomly assign these 21 employees to the 21 days with each person serving on exactly one day. For the following questions think of a continuous list of 21 days, i.e ignore the fact that there are weekend gaps. This year 1 May 2020 is a Friday.

a) In how many ways can this assignment be done if there is no restriction on the order of assignment?

b) In how many ways can this assignment be done if the scientists must serve in a block of 5 consecutive days?

c) In how many ways can this assignment be done if the team leaders must serve in a block of 3 consecutive days and the scientists must serve in a block of 5 consecutive days?

d) In how many ways can this assignment be done if the team leaders must serve on Mondays (there are 4 Mondays)?

Answer 1

yhank you