Question 658653
EXAMINATION has {{{11}}} letters, and in which '{{{A}}}', '{{{I}}}' and '{{{N}}}', all occur twice. {{{11C4}}}, would have been fine if all letters were distinct.

So, we have{{{ E}}},{{{ X}}}, {{{M}}}, {{{T}}}, {{{O}}}, ({{{AA}}}), ({{{II}}}), ({{{NN}}})... {{{8}}} distinct letters.

1. {{{4}}} letters selected, which are {{{all}}} distinct: {{{8C4 = 70}}}
2. {{{2}}} letters alike, and {{{2}}} distinct (eg: {{{AAEX}}}) ={{{ 3C1 * 7C2 = 63}}}
3. {{{2}}} letters alike, and {{{2}}} letters alike (eg: {{{AAII}}}) = {{{3C2 = 3}}}

So answer is,{{{ 70 + 63 + 3 = 136}}}.