Well, honey, I ain't no mathematician, but even I can count those 1's. There are 99 of those bad boys staring back at ya. So, unless you're looking for a lesson in counting, I'd say we're done here.
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There are 210.
56 The number of triples of 1s on 8 bits
Yes, it is. All you need to do is to ensure that there is no repeating pattern in the digits. You could use random numbers to generate a sequence of 1s and 2s but unfortunately, most of these are actually pseudo-random number generators: they generate sequences which pass the tests for randomness up to a point but eventually fail. You could try linking the decision the hoice of 1s and 2s to tosses of a coin or to radioactive decay which are random.Alternatively, you could try1.21121112111121111121111112... where the length of the string of 1s increases by 1 between the 2s.
1 10 11 12 13 14 15 16 17 18 19 21 31 41 51 61 71 81 91 100 There are 21 "1s" between 1 and 100 including 1 and 100.
Basically, this is the same as finding the number of distinct ways of arranging seven 1s and 3 0s. That is (10!/7!3!) = (10*9*8)/(3*2*1) = 120. There are 120 bit strings of length 10 with exactly three 0s.