1. ## Sequence

A bit string is a sequence of zeros and ones. How many bit strings of length
11 can be constructed in each of the following cases?
(a) The strings contain exactly 7 zeros.
(b) The strings contain the sequence 10110.
(c) The strings begin with 010 or end with 110.
(d) The strings begin with 010 and end with 110, and do not contain the sequence 1111.

2. Originally Posted by smithhall
A bit string is a sequence of zeros and ones. How many bit strings of length
11 can be constructed in each of the following cases?
(a) The strings contain exactly 7 zeros.
(b) The strings contain the sequence 10110.
(c) The strings begin with 010 or end with 110.
(d) The strings begin with 010 and end with 110, and do not contain the sequence 1111.

a: 7 zeroes and 4 ones. How many ways are there to rearrange the 4 ones among the 7 zeroes?
b: view the string 10110 as a separate entity D that can appear by itself in different places of the string. in this case Dyx, yDx, yxD for example.
c: The question seems rather vaguely stated, but in this case you should find the number of strings that start with 010 (again, just view this as a seperate entity and inspect the rest of the string only), add to that the strings that end with 110 and from that substract the amount of strings that have both since you counted those twice.
d: as the previous, just view the string inside as a seperate entity, this leaves 11-6 = 5 variables. count the number of ways to make a string with 5 numbers of binary values and substract from that the amount of strings that has a 1111 in it (hint: the middle being 11110, 11111, 01111 and the middle combined with 1 or 2 of the static end, easily countable)