Question

The assignment problem in Linear Programming is also an example of a discrete optimization problem. How many feasible solutions are there to this problem defined on n jobs and n persons?

• A. $n(n-1)$
• B. $n^2$
• C. $n!$
• D. $n^n$

Answer 1

The correct option is C $n!$

$\text{n jobs and n persons}$

First job allotted to a person in n ways.
Second job allocated to a person in (n-1) ways and so on.

$\text{Total number of solutions = n(n-1).........1 = n!}$