Question

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

Answer:

The total number of ways are 168.

Step-by-step explanation:

Consider the provided information.

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.

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:

$3\times 2\times 7=42$

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

$7\times 3\times 6=126$

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