Suppose we want to choose 6 letters, without replacement, from 14 distinct letters. (a) How many...

Suppose we want to choose 6 letters, without replacement, from 14 distinct letters.

(a)	How many ways can this be done, if the order of the choices is not relevant?

(b)	How many ways can this be done, if the order of the choices is relevant?

Solutions

Expert Solution

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.

orchestra answered 1 year ago

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