# combinatorics

• Jan 21st 2010, 08:11 AM
problem
combinatorics
Suppose there are 3 jobs which are to be assigned to 5 mans where each man can be assigned more than 1 job.
How many ways are there to assign the 3 jobs?

My answer is $C(5+3-1,3)$ and my lecturer gives the answer $5^3$.
Can anyone comment on this?
• Jan 21st 2010, 08:46 AM
qmech
The first job can be assigned to any of 5 men.
The 2nd job can be assigned to any of 5 men.
The 3rd job can be assigned to any of 5 men.

The number of possibilities are 5 x 5 x 5.
• Jan 21st 2010, 08:47 AM
Soroban
Hello, problem!

Quote:

Suppose there are 3 jobs which are to be assigned to 5 men
where each man can be assigned more than 1 job.
How many ways are there to assign the 3 jobs?

My answer is $C(5+3-1,\:3)$
and my lecturer gives the answer $5^3$.
Can anyone comment on this?

With no additional restrictions, all 5 jobs could be given to one man.

So, for each of the 3 jobs, there are 5 choices for a man to assign it to.

Therefore, there are: . $5 \times5\times 5 \:=\:5^3$ possible job assignments.

• Jan 21st 2010, 01:35 PM
drumist
Quote:

Originally Posted by problem
Suppose there are 3 jobs which are to be assigned to 5 mans where each man can be assigned more than 1 job.
How many ways are there to assign the 3 jobs?

My answer is $C(5+3-1,3)$ and my lecturer gives the answer $5^3$.
Can anyone comment on this?

Your solution of $\binom{5+3-1}{3}$ would have been correct if the jobs were indistinguishable, i.e., if we only cared how many jobs each person received as opposed to which jobs they received. But that does not appear to be the case in this particular problem. Does that clear it up any?