Permutations of a Four Letter Word
In this piece of coursework my initial aim is to investigate how many
different combinations there are for four letters (e.g. ABCD), I also
intend to develop this to investigate the way in which by altering the
letters to form other kinds of combinations (e.g. ABCC or AAB) the
number is affected. Once I have found the general formulae, I will
apply these to harder situations and this is what I am aiming to do. I
am trying to find the general formulae which can be applied to all
situations we set about this by looking at the simplest scenario first
i.e. one letter (e.g.A) moving on to harder problems and by the end I
hope to be able to find the possible arrangements for any given word.
I will do this by using tables and lists of my results to show the
possible combinations and make it easy to compare them and to spot the
pattern and try and turn this into a general formula. Once the initial
formulae have be en discovered I think that it should be much easier
to determine the harder formula, as I will not need to write out as
many tables, to work out these formulae
Results-
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Single different letters-
=========================
1 letter- A
2 letters- AB
BA
3 letters- ABC
ACB
BAC
BCA
CAB
CBA
No. of letters 1 2 3
No. of combinations 1 2 6
This gives the formula =n! - Where n equal the number of letters
Explanation-
============
This is because once you have picked one letter there are then only
two more letters and then one letter. This means that you get 3x2x1
and this gives you 6 which is equal to n!
This formula will allow me to work out the number of combinations of
any word without a repeated letter by using this basic idea I will be
come with a goal in life - to succeed on it. With that kind of mentality I
Although facing challenges head-on may seem daunting at times, and taking the easy way out can have grand appeal, the rewards at the end of the hard path are infinitely greater.
and gain strength with all experiences that you go through. This is evident when Ulti...
attitude is just as important as achieving the goal, and one must want to achieve that
The data we gathered from our analysis are presented in a formal way on the following page.
This skill will enable oneself to identify the situations thoroughly and act accordingly when things are
The tools that are in place to deal with these challenges come in many different forms. For example, in handling family responsibilities, I have a very
When taken out of the fixed mindset and placed within the growth mindset, sometimes all that is needed is someone to believe that you have the ability to achieve. Dweck discloses that every
...ly in the future I want to be mentally prepared for extra workload and the possibility of conflict in any given situation.
As I 've mentioned before, self-improvement really comes down to daily habits and the compounding effects of them.
Habit one of highly effective people is being proactive. What I learned from habit one is that we are in charge of our lives. We must be proactive and take responsibility for our actions and choices. I learned that I must take the initiative and recognize my responsibility to make things happen. I must be the one to act and not be acted upon. This habit taught me that in order for me to be effective I must first be proactive. If I am not proactive it makes it almost impossible for me to be effective. If people take a passive stance, they
In order to do this, I must be proactive. Being proactive means that in between the stimulus and response, there is a third stage. This stage is the freedom to choose, and it is full of self awareness, imagination, conscience, and independent will. Being proactive means that when I feel an impulse, I am able to make that impulse subordinate to the values I hold inside. I am still influenced by the stimuli, but I am aware of this influence and choose how I react to it. An outside stimulus can only affect me so much as I let it. It is not outside forces that help or hurt me, it is my reaction to those outside forces. My character, my basic identity, can only be impacted if I let it. By understanding that my most difficult experiences become the crucibles that forge my character, I can turn any circumstance in my favor. My basic nature is to act, rather than be acted upon. This is why it is key to take the initiative in every situation. Taking initiative means recognizing my responsibility to make things
them and think of ways to keep going without them affecting me on my way to reach my goal.
These are just some but the most important personal effectiveness skills which make the achievement of any goal easier and less costly.