SOLUTION: how many bit string of length eight either start with a 1 bit or end with the two bits 00

Question 401664: how many bit string of length eight either start with a 1 bit or end with the two bits 00
Found 2 solutions by Alan3354, Jk22:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
how many bit string of length eight either start with a 1 bit or end with the two bits 00
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Starting with the 1 bit = 128 to 255 = 128 numbers
Ending with 00 = 256/4 = 64 numbers
Half of these 64 numbers start with 1, leaving 32.
Assuming starting with 1 and ending with 00 is counted only once:
128 + 32 = 160 numbers

Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!

We add the possibilities : if it starts with bit 1, but does not stop with 00 in order not to count doubly, we get : 2^5 for bits 2,3,4,5,6, times 3 possibilities for bits 7,8 should not equal 00, hence 32*3

these possibilities have to be added to all cases where the first bit is 0, and the 2 last 00, which makes bits 2,3,4,5,6 free, or 2^5=32

the total number of possibilities are then : 32*4=64*2=128 possibilities.
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