combinatorics

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January 21st 2010, 07:11 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?
January 21st 2010, 07:46 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.
January 21st 2010, 07:47 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?

Here is your lecturer's reasoning:

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.
January 21st 2010, 12:35 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?