**Quote:**

In a lottery there are 900 tickets numbered consecutively 100, 101, ..., 998, 999. If a ticket is drawn at random, what is the probability that

(i) the three digits are neither in ascending or descending consecutive order (e.g. not of the form 345 or 765),

(ii) the three digits read the same backwards and forwards?

Please provide your calculation with your answer.

i) 1-p(the 3 digits are in ascending or descending order)

there are 7 such numbers in ascending order and 7 such numbers in descending vis a vis

123, 234, 345, 456, 567, 678 & 789 (the same set of numbers in reverse order)

p = 1 - 14/900 = 886/900

ii) there are 9 such numbers

111, 222 ..... 999

p = 9/900 = 1/100