1. ## Permutation help needed

A set of 4 letter passwords is to be constructed. Identify the number of password if:
i) All 26 letters of the alphabet can be used without any restrictions.
ii) All 26 letters of the alphabet can be used, but no letter can be used more than once.
iii) The passwords are constructed using only two of the letters from the set {x,y,z}

I have worked part i) and ii) but im struggling to work out part iii). Can anyone help me out with this. Thanks.

2. Originally Posted by alpha
A set of 4 letter passwords is to be constructed. Identify the number of password if:
iii) The passwords are constructed using only two of the letters from the set {x,y,z}
The answer depends upon what the question means.
Could it be XXXY or XXZZ? Or either?

3. I am not sure but I tink it could be either. Thanks

4. OK then.
There are $\displaystyle 3\cdot\frac{4!}{(2!)^2}$ of the type XXYY.
There are $\displaystyle 3\cdot\frac{4!}{3!}$ of the type XXXZ.
Do you why?

5. No sorry.

6. Originally Posted by alpha
No sorry.
Do you understand that the string $\displaystyle XXXYYZ$ can be rearranged in
$\displaystyle \frac{{6!}}{{\left( {3!} \right)\left( {2!} \right)}}$ ways?