The number of sequences of length five with 0 and 1 as terms which contains atleast 2 consecutive zeroes is..??....I am getting 20 as the answer but the answer is 19..plz help..thanx in advance...!!!!
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The sequence of length 5 is to be composed of only 0's and 1's. Consider the cases depending on how many 0's comprise the sequence, and the number of possible sequences with at least 2 consecutive zeroes for each case-
0 0's - 0 sequences
1 0's - 0 sequences
2 0's - 4 sequences
3 0's - 10 sequences
4 0's - 5 sequences
5 0's - 1 sequence.
Thus, there are 20 such sequences. And I too got the same answer as you did. However, if we are forced to accept 19 as the correct answer, then one possible explanation is to not include the 5 0's case as that doesn't have any 1; assuming the sequences have to have both 0's and 1's.
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