Answers will vary, as there are many possible ways to do this. One possibility is to take the 100 pictures of the sub-regions, shuffle them thoroughly, then look at the first 10. Another is to assign each sub-region to a number from 00 to 99, and use the last two digits of the daily lottery number for each of the last 10 days. A commonly used method for assigning regions to numbers is to use a random-number-generating device, such as a calculator, a die, or computer software.
With a calculator, the first two decimal digits of the random number will range from 00 to 99, and each of the 100 values is equally likely. If a number appears more than once, it is rejected, so that 10 different sub-regions are selected. Another idea is to use a 10-sided die or spinner and to generate two random digits by two tosses or spins (and get your 10 random numbers by 20 tosses or spins).
While it is possible for the two estimates to be equal, it is pretty unlikely, due to the variation in the individual sub-regions. If the number of sub-regions in the sample increases to 20, the variation in the estimates should be reduced. The estimates should be closer to the actual value, but it is no more likely that they will be equal.