Saturday, April 4, 2009

PERMUTATON AND COMBINATIONS,10!=10P10.

All possible arrangaments of 10!=10p10=permutation of 10! i.e 3628800 arrangaments.
10!=10x9x8x7x6x5x4x3x2x1=3628800.
9!=9x8x7x6x5x4x3x2x1=362880.
8!=8x7x6x5x4x3x2x1=40320.
7!=7x6x5x4x3x2x1=5040.
6!=6x5x4x3x2x1=720.
5!=5x4x3x2x1=120.
4!=4x3x2x1=24.
3!=3x2x1=6.
2!=2x1=2.
1!=1
0!=zero and itself=only 0=one possible way =1.

Permutation that is arrangement of 10! =10p10
Applications :
1).Allocation of cell numbers to mobile users with out repetition of 0-9 numbers=10p10=10!.
2).Coding of alphabetics in factorial ways in any language to reveal secrets.
3). Vikram's film Aparichithidu can reveal the possible understanding of permutation that is arrangement in fatorial ways but mistakely spelled in the film
as combination=khumbipakam=telugu literature(language) .
4)Combination easily reveals that it should be two numbers arrangement like binary numbers '0' and '1' or a group of two different objects, numbers,symbols etc
5)Repitition of numbers or objects or symbols make more possible arrangements as it is obseved in case of cell numbers.

9876543210 is cell number =All possible ways of arrangements is 10p10=10!
0!=0x1=0=1 possible way=1.
1!=1x1=1
2!=2x1=2
3!=3x2=6
4!=4x6=24
5!=5x24=120
6!=6x120=720.
7!=7x720=5040.
8!=8x5040=40320.
9!=9x40320=362880.
10!=10x362880=3628800.
The result of first factorial arrangement is multiplied to the next factorial arrangement is observed in the in the second factorial arrangement.Order of sequence in all the posssible arrangements that is n! substitute numbers 0-9 is easy to make the possible arrangement to define permutation of numbers.
generally permutation is represented by "P".
and combination is represented by "C".

1 comment:

  1. ranadheer kumar palakurthi.b.tech (2005-2009)
    ganapathy engineering college (jntu affiliated),rangashaipet , warangal
    pin code 506005

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