Question

There are 25 applicants for four jobs; Computer Programmer, SoftwareTester, Manager, and Systems Engineer.This is an example of ___? (Combination or permutation?)n= ____?r= ____?There are ____ ways to choose applicant for the positions of a computer programmer, software tester, manager,and systems engineer.

Answer 1

Step 1

Permutations

Permutation means total number of ways in which we can arrange elements in The combination order combination.

Combinations

The combination means a total number of ways in which we can select some elements from a given set of elements.

Permutations are orderings, while combinations are choices.

Step 2

Combination

Step 3

n = 25

r = 4

`\begin{gathered} Number\text{ of ways} \\ ^(25)C_4\text{ = }(25!)/((25-4)!4!)\text{ } \\ =\text{ }\frac{25!}{21!\text{ }*\text{ 4!}} \\ =\text{ }\frac{25\text{ }*\text{ 24 }*\text{ 23 }*\text{ 22}}{4*3*2*1} \\ =\text{ 12650 ways} \end{gathered}`

Final answer

Combination

n = 25

r = 5

12650 ways