In: Statistics and Probability
Suppose we want to choose 6 letters, without replacement, from
14 distinct letters.
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So to choose 6 out of 14 letters in two different scenarios:
i) If the order of the choice is not relevent, to illustrate this lets take an example
The order of choice is not relevent implies that suppose A,B,C,D,E,F are 6 letters chosen from 14 different letters then
A,B,C,D,E,F and F,E,D,C,B,A are basically the same that is they would just bee counted as 1 because the elements are same just the order is different.
So in this case combination would be used that is to choose 6 out of 14 letters the number of ways are:
Hence there are 3003 ways to choose 6 out of 14 letters if orders didn't matter.
ii) iIf order matters
This implies that A,B,C,D,E,F and F,E,D,C,B,A are different because the elements are same but the order is different, and order matters in this case.
Here n=14
r=6
so instead of combination permutation would be used here and it is given by
Hence there are 2162160 ways to choose 6 out of 14 letters if order matters.