Question

Of the 9 new programmers hired by a software company, 3 will work on web applications, 4 will work on desktop applications, and 2 will work on mobile applications. In how many ways can this arrangement be made?

Answer 1

There are 1,260 different ways to arrange the 9 new programmers for web, desktop, and mobile applications.

Explanation:

To determine how many ways you can arrange the 9 new programmers for different applications, you can use permutations. Specifically, you can use the concept of permutations with repetitions, as there are different categories (web applications, desktop applications, and mobile applications) with a specific number of programmers assigned to each category.

The formula for permutations with repetitions is:

P(n; n1, n2, n3, ..., nk) = n! / (n1! * n2! * n3! * ... * nk!)

Where:

n is the total number of items to be arranged (in this case, 9 programmers).

n1, n2, n3, ... are the numbers of items in each category (3 for web, 4 for desktop, and 2 for mobile).

Now, let's calculate it:

P(9; 3, 4, 2) = 9! / (3! * 4! * 2!)

Calculate the factorials:

9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880

3! = 3 * 2 * 1 = 6

4! = 4 * 3 * 2 * 1 = 24

2! = 2 * 1 = 2

Now, plug these values into the formula:

P(9; 3, 4, 2) = 362,880 / (6 * 24 * 2)

P(9; 3, 4, 2) = 362,880 / 288

P(9; 3, 4, 2) = 1,260

So, there are 1,260 different ways to arrange the 9 new programmers for web, desktop, and mobile applications