Question

How many ways are there to assign six jobs to five different employees if every employee is assigned at least one job?

Answer 1

Answer:

There are 1800 different ways.

Step-by-step explanation:

A permutation give as the total ways in which we can organized a group of elements where the order is important. So, the  permutation of n elements when all of them are not different is calculate as:

$\frac{n!}{n1!n2!...nk!}$

Where k is the number of elements that are different, n1, n2, ... nk are the number of times that very element appears and n is equal to n1+n2+...nk.

In this case we have 5 differents and general ways to assign six jobs to five different employees:

1. the first employee receive 2 jobs

2. the second employee receive 2 jobs

3. the third employee receive 2 jobs

4. the fourth employee receive 2 jobs

5. the fifth employee receive 2 jobs

Then, if the first employe receive 2 jobs, its mean that we have six people to permutate and the first person appears two times.

So the permutation of this 6 element in which one is repeat 2 times is calculate as:

$\frac{6!}{2!*1!*1!*1!*1!*1!}=360$

Therefore, there are 360 ways to organized five different employees into 6 jobs where the first person can receive two jobs.

For the other 4 options we can made the same calculation, so the total number of ways that we can organized five employees in six jobs are calculate as:

360*5=1800

Finally there are 1800 different ways.