Question

In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?

Answer 1

Hint: A can be assigned any of the three jobs. So, there are 3 ways of assigning a job to A. B can now be assigned any of the two remaining jobs in 2 ways and C can now be assigned the job in 1 way. So, the required number of ways can be calculated by multiplication.

Complete step-by-step answer:
Here, we can see that A is capable of doing any 3 jobs. But A has to choose only one job. We can see that if A does any job then only the remaining 2 jobs are available for person B.
B can be assigned any job of the remaining two jobs. So, B can be assigned any one job of the remaining two jobs.
We can see that C has only one job left. So, C can be assigned only one job.
Total number of ways in which the jobs can be assigned to three persons A, B and C\[=3\times 2\times 1=6\] .

Note: This can also be solved in another way. We have 3 jobs and 3 people also. We can think of rearrangements of jobs. We know that the rearrangement of n is \[n!\] . So rearrangement of three jobs will be \[3!\].