Question

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?

Answer #1

answer

A) 2 raised to power 12

B) 2048

C) 448

How many bit strings of length 12 contain the substring
"111000"?

Discrete Math
a.) How many bit strings are there of length five or less, not
counting the empty string?
b.) How many different three-letter initials with none of the
letters repeated can people have?
c.) How many different three-letter initials are there that
begin with the letter B?
d.) How many 5-element DNA sequences end with
A?
e.) How many bit strings of length nine both begin and end with
1?

(a) Find a recurrence relation for the number of bit strings of
length n that contain the substring
10.
(b) What are the initial conditions?
(c) How many bit strings of length seven (i.e.
a7) contain the substring
10?

(a) How many 12-bit strings contain exactly five 1's?
(b) How many 12-bit strings contain at least nine 1's?
.(c) How many 12-bit strings contain at least one 1?
(d) How many 12-bit strings contain at most one 1?

For a bit string containing 10 bits, how many strings are there
that contains 5 consecutive 0s or 1s.
The OR is inclusive in this example and it is AT LEAST 5
consecutive so 6 consecutive would still count.
I don't understand how I should approach this. There are too
many cases to exclude when calculating the permutation of a single
case.

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...

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

How many binary strings of length 15 contain the same
bit in all the odd numbered positions? The positions are numbered
1, 2, . . . , 15. Show how you arrived at your answer, which rules
of counting were used etc.
Thank You

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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