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

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MrRoyal MrRoyal · Answer 1 · 2021-03-23T08:21:07+01:00

Answer:

168 ways

Step-by-step explanation:

Given

[tex]Junior = 7[/tex]

[tex]Senior = 3[/tex]

Required

Number of ways 3 project can be assigned

Starting with the second project.

This can be assigned to only senior coders

So:

[tex]n_1 = 3[/tex]

Then, the third project.

This can be assigned to only junior coders

So:

[tex]n_2 = 7[/tex]

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

Since the first can be assigned to anybody.

[tex]n_3 =2+ 6[/tex]

[tex]n_3 =8[/tex]

The number of selection is then calculated as:

[tex]n = n_1 * n_2 * n_3[/tex]

[tex]n = 3 * 7 * 8[/tex]

[tex]n = 168[/tex]