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How many bit strings of length 10 have more 0s than 1s?
There are 210.
How many bit strings of length 8 contain exactly three 1's?
56 The number of triples of 1s on 8 bits
Is it possible to build an irrational number whose decimal digits are just 1's and 2's?
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.
How many 1 ' s are there in digits from 1 to 100?
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.
How many bit strings of length 10 have exactly three 0s?
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.
