Express the series in summation notation. 2 + 4 + 6 + 8 + 10 + 12
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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:
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:
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.