Question 937902
 the number of ways to arrange the three letters in the word CAT in different two-letter groups where CA is different from AC and there are no repeated letters because order matters, we're finding the number of permutations of size {{{2}}} that can be taken from a set of size {{{3}}}

this is   written as {{{3P2}}}

{{{3P2=n!/(n-r)!}}}  

{{{3P2=3!/(3-2)!}}}  

{{{3P2=(3*2*1)/1}}}  

{{{3P2=3*2*1}}}  

{{{3P2=6}}}  - the number of permutations of size {{{2}}} that can be taken from a set of size {{{3}}}

We can list them as:

    {{{CA }}}  {{{CT}}}   {{{AC}}}   {{{AT}}}   {{{TC}}}   {{{TA}}}