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PS Archive | Counting

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Counting : We have n numbers From 1 to n(All are included). We will fix m numbers from first k numbers & among k numbers as the m numbers are fixed so remaining (k-m) can not stay its original position say 4 can not stay at 4th position in any permutation. How many ways are there to arrange them?
Example: n=10,k=6,m=3;
So first we think 1 2 3 are fixed in their own positions. so we have 7 numbers. Any number can be kept at 4th position except 4 and this rule will be continued for first k places.
And
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