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?

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.

For second project we have 3 choices and for third project we have 7 choices.

Now there are 2 possible case:

Case I: If first and second coder is senior, then the total number of ways are:

[tex]3\times 2\times 7=42[/tex]

Case II: If first and third coder is junior, then the total number of ways are:

[tex]7\times 3\times 6=126[/tex]

Hence, the total number of ways are: 42+126=168