Question

How many ternary strings of length 8 begin with 01 or end with 1? (A ternary string consists of 0s, 1s, and 2s.)

Answer #1

We know length of string that is 8.

We want to start with 01 or end with 1

So let us consider the string which starts with 01 so we are
left with 6 places to fill with 0s, 1s and 2s. There are 3
possibilities for each place hence total number of such string will
be 3^{6}.

Now we want our string to end with 1. There are 7 places left to
fill with 0s, 1s and 2s. So each place has 3 possiblities hence
there are 3^{7} such strings.

Since we want either of the strings. We will add both and hence
there are 3^{6} + 3^{7} =
4*3^{6} strings of length 8 which begin with 01 or
end with 1.

1. (4 pts) Consider all bit strings of length six. a) How many
begin with 01? b) How many begin with 01 and end with 10? c) How
many begin with 01 or end with 10? d) How many have exactly three
1’s? 2. (8 pts) Suppose that a “word” is any string of six letters.
Repeated letters are allowed. For our purposes, vowels are the
letters a, e, i, o, and u. a) How many words are there? b)...

3))Find a recurrence relation for the number of ternary strings
of length ? ≥ 1 that contain at least two 0s. What are the initial
conditions?

how many 8 bit strings begin or end with 1 ?
* Is there a simple way of solving this problem ?*

How many bit strings of length 20 are there that contain eight
1s and twelve 0s so that each 1 is followed by one 0
immediately?

1. Solve the following two " union " type questions:
(a) How many bit strings of length 9 either begin with 2 0s or
end with 2 1s? (inclusive or)
(b) Every student in a discrete math class is either a computer
science or a mathematics major or is a joint major in these two
subjects. How many students are in the class if there are 30
computer science majors (including joint majors), 20 math majors
(including joint majors) and...

1) A candy store sells five different flavors of jelly beans. In
how many way can we fill a bag with 100 jelly beans
2) How nay ternanry strings ( consisting of 0s, 1s and 2s) of
length 20 can be formed if at least one of the last three digits
must be a 1

This is a Discrete math problem.
a. How many bit strings of length 12 are there in total?
b. How many bit strings of length 12 contain an odd number of
1s?
c. How many bit strings of length 12 contain “111000” as a
substring of 6 consecutive bits in a row?

(1) How many bitstrings of length 8 begin with two 1’s or end
with three 1’s?
(2) How many bitstrings of length 10 contain three consecutive
0’s or 4 consecutive 1’s?

Assume strings contain ONLY the letters: a, b.
How many bit strings of length 8 either start with bbb or end
with aa ?

Consider strings of length 8 made up of elements in {0,1}.
How many strings contain 000 as a substring?
How many strings contain more 0’s than 1’s?

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