Question 1204716
permutations of { {{{A}}},{{{ A}}}, {{{A}}}, {{{B}}}, {{{B}}},{{{ B}}}, {{{C}}}, {{{D}}} }

there are {{{8}}} letters
there are {{{3}}} {{{A}}}s and {{{3}}} {{{B}}}s, since order matters, there will be following number of permutations  :


{{{nPr=n!}}}/({{{n[1]!}}}*{{{n[2]!}}}*....*{{{n[r]!}}})


{{{n=8}}}

Distinct subsets:

Subsets : {{{A = 3}}}; {{{B = 3}}}; {{{C = 1}}}; {{{D = 1}}};
Subsets' count: {{{n[1](A) = 3}}}, {{{n[2](B) = 3}}}, {{{n[3](C) = 1}}}, {{{n[4](D) = 1}}}


{{{nPr=8!/(3!*3!*1!*1!)=(8*7*6*5*4*3*2*1)/(3*2*1*3*2*1*1*1!)=8*7*5*4=56*20=1120}}}

The letters of the word {{{AAABBBCD }}}can be arranged in {{{1120}}} distinct ways.