Computer Science, asked by farhan9341, 1 year ago

How many bit strings of length 10 contain either five con- secutive 0s or five consecutive 1s?

Answers

Answered by aqsaahmed19945
19

Observe first 5 consecutive 0s


Summation rule: the first 5 consecutive 0’s could start at position 1, 2, 3, 4, 5, or 6


Start at first position


Other 5 bits can be anything: 2^5 = 32


Start at second position


First bit must be a 1


There are various possibilities that can be included in it.


Remaining bits can be anything: 2^4 = 16


Start at third position


Second bit must be a 1 due to above mentioned reason.


First bit and last 3 bits can be anything: 2^4 = 16


Starting at 4,5 and 6 positions


Same as starting at positions 2 or 3: 16 each


Total = 32 + 16 + 16 + 16 + 16 + 16 = 112


The five consecutive 1’s ensue the same pattern, and have different like 112 possibilities


There would be two cases counted twice (that we thus need to exclude): 0000011111 and 1111100000


Total = 112 + 112 – 2 = 222



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