Question

A project manager must select four analysts from her group to write four

different software functions. There are 5 junior and 8 senior analysts in her group.

The first and fourth functions can be written by any of the analysts. The second

function must be written by a senior person and the third function must be written

by a junior person. How many ways are there for her to assign the analysts to the

functions if no person can be assigned to more than one function?

Answer 1

Using the Fundamental Counting Theorem, it is found that there are 4,440 ways to assign the analysts.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem:

• With the first function being written by a senior, we have that: $n_1 = 8, n_2 = 7, n_3 = 5, n_4 = 10$.

• With the first function being written by a junior, we have that: $n_1 = 5, n_2 = 8, n_3 = 4, n_4 = 10$.

Hence:

N = (8 x 7 x 5 x 10) + (5 x 8 x 4 x 10) = 4400.

There are 4,440 ways to assign the analysts.

To learn more about the Fundamental Counting Theorem, you can check https://brainly.com/question/24314866