Observe first 5 consecutive 0 s Summation rule: the first 5 consecutive 0 's could start at position 1,2,3,4,5, or 6 Start at the first position Other 5 bits can be anything: 25=32 Start at the second position The first bit must be a 1 There are various possibilities that can be included in it. Remaining bits can be anything: 24=16 Start at third position The second bit must be a 1 due to above-mentioned reason. First bit and last 3 bits can be anything: 24=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