How many digit number greater than 200 but less than 300 can be obtained from 1234,and what is the probability that a number choosen at random falls into this range

Answer 1

If 200<n<300, then the first digit must be 2. That leaves 4 digits for each of the remaining digits for a total of m=1*4*4*4 numbers.
If there is no limitation, the number of all possible (distinct) numbers is
N=4^4.

The probability that a number formed by the digits 1,2,3,4 will fall into that range is therefore m/N.