Question

Exercise 8.3.4: Selecting coders for 3 different projects. About (a) A manager must select three coders from her group to write three different software projects. There are 7 junior and 3 senior coders in her group. The first project can be written by any of the coders. The second project must be written by a senior person and the third project must be written by a junior person. How many ways are there for her to assign the three coders to the projects if no person can be assigned to more than one project

Answer 1

168 ways

Explanation:

Given

`Junior = 7`

`Senior = 3`

Required

Number of ways 3 project can be assigned

Starting with the second project.

This can be assigned to only senior coders

So:

`n_1 = 3`

Then, the third project.

This can be assigned to only junior coders

So:

`n_2 = 7`

At this point, we are left with 2 senior coders and 6 junior coders

Since the first can be assigned to anybody.

`n_3 =2+ 6`

`n_3 =8`

The number of selection is then calculated as:

`n = n_1 * n_2 * n_3`

`n = 3 * 7 * 8`

`n = 168`