|Fundamental Counting Principle|
Example 1: Let there be three jobs a, b, c and three persons A, B and C. Find the possible number of assignments of jobs so that one person is assigned only one job.
Solution: Let us start with person A. A can be assigned the remaining jobs in the way shown in the following tree diagram as shown below
The first set of branches of the tree shows that A can be assigned any one of the three jobs(a, b, c). Then for each one of these we can assign either of the two remaining jobs to B shown by the second set of branches of the tree. For each one of these two jobs there is only one job left at the end, which can be assigned to C.
The persons A, B and C can be assigned the three jobs a,b,c in six different ways as shown.
Directions: Solve the following.