A workman has six jobs to do. In how many different orders can he do them?
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Introduction
There are six jobs- A, B, C, D, E and F. They are to be done in some order. In how many different orders can they be done?
The answer is that there are 720 ways in which the six jobs can be done. This is because there are six ways in which the first job can be chosen, five ways in which the second job can be chosen (as the first job has already been chosen), four ways in which the third job can be chosen and so on. Therefore, the number of ways of choosing six jobs from six is 6 × 5 × 4 × 3 × 2 × 1 = 720.
The six jobs
The six jobs can be done in any order. For example, the workman could do job 1 first, then job 2, job 3, job 4, job 5, and job 6. Or, the workman could do job 3 first, then job 6, job 4, job 1, job 5, and job 2. In how many different orders can the workman do the six jobs?
There are 6! = 6×5×4×3×2×1 = 720 possible orders in which the workman could do the six jobs.
The different orders
There are 6! = 720 different orders in which the six jobs can be done.
Why it matters
Why the order in which you do things matters
You probably have a to-do list that you try to complete every day. It might look something like this:
-Get out of bed
-Brush your teeth
-Eat breakfast
-Get dressed
-Commute to work
-Start work
The order in which you do these things might not seem important, but it can actually make a big difference in your day. For example, if you eat breakfast before getting dressed, you might end up getting your clothes dirty. Or if you start work before commuting, you might get stuck at the office all day.
The order in which you do things can also affect your mental and emotional state. For example, if you start your day by checking social media, you might get stressed out by all the news and notifications. Or if you eat breakfast after getting dressed, you might feel rushed and stressed out.
It’s important to think about the order in which you do things because it can have a big impact on your day. Sometimes it’s helpful to switch up the order of your to-do list to see if it makes a difference.
How to optimize
There are six! possible ways to order the six tasks:
1. Dig the hole, plant the tree, lay the paving stones, build the wall, paint the fence, mow the lawn.
2. Dig the hole, plant the tree, lay the paving stones, build the wall, mow the lawn, paint the fence.
3. Dig the hole, plant the tree, lay the paving stones, build the wall, paint the fence, mow lawn.
4. Plant tree, dig hole, lay paving stones, build wall, paint fencemow lawn.
5. Plant tree ,dig hole ,lay paving stones ,build wall ,paint fence ,mow lawn.
6. Paint fence ,mow lawn ,plant tree ,dig hole ,lay paving stones ,build wall
Conclusion
There are six jobs to do, which we’ll call J1 through J6. To figure out how many different orders the workman can do them in, we use what is called the “permutations” formula. The permutations formula tells us that the number of ways P(n,r) that r objects can be selected from n possibilities is:
P(n,r) = n!/(n-r)!
For our six jobs, there are 6!/(6-6)! = 6!/0! = 6! = 720 different ways the workman could do them.
