I am interested in arrangements of MATHEMATICS
with
both T's before both A's or
both A's before both M's or
both M's before the E
I define the following sets
= {arrangements with both T's before both A's}
= {arrangements with both A's before both M's}
= {arrangements with both M's before E}
I am able to find the cardinality of everything else but
i.e. arrangements with both T's before both A's and both M's before E.
I know I want to pick four of the 11 spots (11 choose 4)
and arrange H,I,C,S in those spots (4! ways)
But I dont know whaat to do next, I can't place only the T's in the two left most spots because certainly go T,M,M,E,T.
Thank you for your help.