Discrete Math: How many bitstrings of length of 5 start or end with 11
Discrete Math:
How many bitstrings of length of 5 start or end with 11.
bit string : means string must contains either 0 or 1
now, we have to find number of bit strings of length 5 that start or end with 11
first lets find number of bits strings of length 5, start with 11 : 1 1_ _ _ : we have 3 positions to fill at the end and we have two options to fill 0 or 1: 2*2*2 = 8 ways to fill 3 positions with 0 or 1
so, number of bits strings of length 5, start with 11 are: 8
now, the number of bits strings of length 5, end with 11 : _ _ _ 11 : we have 3 positions to fill at the beginning and we have two options to fill 0 or 1: 2*2*2 = 8 ways to fill 3 positions with 0 or 1
so, number of bits strings of length 5, end with 11 are: 8
now, the number of bits strings of length 5, that start and end with 11 are included in both cases above, so we have to remove once
the number of bits strings of length 5, that start and end with 11 are: 11 _ 11 : 2
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