There are two different interpretations of "keeps letters RIT together".

What about RTI, TRI, TIR, ITR, and IRT.  The lettrers are together but
not in the same order, but the problem doesn't say they must be in the
same order.  They are still together even though not in the original order.  

Interpretation 1:  They are in the same order RIT.

That's the number of arrangements of these 7 things

A, L, G, O, RIT, H, M.

That's 7!

For the probability of selecting one of those, 7! is the numerator

we need a denominator, which is 9!  

Probability 7!/9! = 5040/362880 = 1/72

Interpretation 2:  Multiply both resuts of interpretation 1 by 3!

7!*3! = 5040*6 = 30240

30240/362880 = 1/12

Edwin