a)  Keeping TT together means the TT can be treated as if it is a 

 single, unique,letter itself.  Call this {TT}, where the brackets are

used to indicate the letters that must be grouped.  



The number of arrangements is effectively the same as that of 5 unique

letters:  5! = 120.   So the number of SIX letter arrangements where TT

must stay together is .





b)  Keeping MTTR together --  I am assuming the letters {MTTR} themselves

can be shuffled but the four letters must remain together as a group.  

The letters {{MTTR},A,E} can be arranged in 3! = 6 ways and for EACH ONE 

of these arrangements, you can arrange {MTTR} in 4!/2! = 12 ways.  Thus 

there are 6*12 =  ways to arrange the  letters of MATTER, 

where the letters MTTR are kept together, but are shuffled amongst themselves. 

   

 

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