Question

How many ways can you arrange $26$ letters?

Answer 1

Finding the arrangement :

Number of arrangement for $n$ element $=n!$ without any repetition

Also we know that $n!=n\times (n-1)\times (n-2)\times ....\times 4\times 3\times 2\times 1$

Therefore arrangement of $26$ letter in $26!$

Using above formula for $26!=26\times 25\times 24\times ....\times 4\times 3\times 2\times 1$

Hence , the arrangement of $26$ letter is $\mathbf{26}\mathbf{!}\mathbf{}\mathbf{=}\mathbf{}\mathbf{67}\mathbf{,}\mathbf{108}\mathbf{,}\mathbf{863}\mathbf{}$