After typing the first letter, there are 25 letters remaining; after the first two, there are 24, and so on. For 10 unrepeated letters then there are 25*24*23*...*16 divided by the number of ways of arranging the same 10 letters=10*9*7*...*2*1=5,311,735. The number of possible ways of arranging 10 letters is 26^10=1.41167*10^14 with and without repeats. So the probability of no repeats is 5311735/1.41167*10^14=3.763*10^-8.