帮我解道题吧，排列组合的....

salabomUID: 2115099

How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s ???

answer is 147. why ?

george7333UID: 2131837

my means is TOO complicated......:funk:
both 3 consecutive 0s and 4 consecutive 1s:
3 0s and 5 1s: 4
4 0s and 4 1s: 4
total: 8
3 consecutive 0s:
3 0s and 5 1s: 6
4 0s and 4 1s: 25
5 0s and 3 1s: 40
6 0s and 2 1s: 27
7 0s and 1 1s: 8
8 0s and 0 1s: 1
total: 107
4 consecutive 1s:
0 0s and 8 1s: 1
1 0s and 7 1s: 8
2 0s and 6 1s: 18
3 0s and 5 1s: 16
4 0s and 4 1s: 5
total: 48
so the answer is:
107+48-8=147