Question

How many strings of six letters are there?

Short answer

$308,915,776$There are strings of six letters.

Step-by-step solution

Step 1: Definitions

Definition of Permutation (Order is important)

No repetition allowed:$P(n,r)=\frac{n!}{(n-r)!}$

Repetition allowed:$n^T$

Definition of combination (order is important)

No repetition allowed:$C(n,r)=\left(\begin{array}{l}n\\ r\end{array}\right)=\frac{n!}{r!(n-r)!}$

Repetition allowed:$C(n+r-1,r)=\left(\begin{array}{c}n+r-1\\ r\end{array}\right)=\frac{(n+r-1)!}{r!(n-1)!}$

with$n!=n(n-1)\cdot .....\cdot 2\cdot 1$

Step 2: Solution

The order of the elements matters (since we want to select the elements in order), thus we need to use the definition of permutation.

The alphabet contains 26 letters

We are interested in selecting r = 6 elements from a set with n = 26 elements.

Repetition of elements is allowed.

$n^{\gamma }={26}^6=308,915,776$

Thus there are $308,915,776$ways in which six elements can be selected in order from a set with twenty-six elements when repetition is allowed.