An arrangement is called a Permutation. It is the rearrangement of objects or symbols into distinguishable sequences. When we set things in order, we say we have made an arrangement. When we change the order, we say we have changed the arrangement. So each of the arrangement that can be made by taking some or all of a number of things is known as Permutation. The word arrangement is used to emphasize that the order of the things is important.
Consider the three letter word 'PEN'. In how many ways can we rearrange it?
PEN PNE EPN ENP NEP NPE
A three letter word can be arranged in 6 ways. You can easily find it out. How about a 10 letter word. Quite a long process, isn’t it? Hence we use FACTORIAL to find the number of possible ways to arrange the elements.
For a 3 letter word,
3! = 3*2*1 = 6 ways.
For a 10 letter word,
10! = 10*9*8*7*6*5*4*3*2*1= 3628800
There are many applications of permutations in everyday life. One is a license plate. License plates are a permutation because the order matters. Another application of permutations is telephone numbers. For example, if you dialled 123-4567 you'd get a different person than when you dialled 765-4321.
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Mathematics