Question

How many bits strings of length 12 contain (8 pts)? a. exactly three 1s? b. at most three 1s? c. at least three 1s? d. an equal number of 0s and 1s?

Answer 1

1. Exactly three 1 s?

$\left(\begin{array}{c}12 \\3\end{array}\right)=220$

2. At most three$1 \mathrm{~s}$ ?

$\left(\begin{array}{c}12 \\0\end{array}\right)+\left(\begin{array}{c}12 \\1\end{array}\right)+\left(\begin{array}{c}12 \\2\end{array}\right)+\left(\begin{array}{c}12 \\3\end{array}\right)=1+12+66+220=299 \text {. }$

3. At least three 1 s?

Take a shortcut by using the previous answer:$2^{12}-66-12-1=4017$

4. An equal number of$0 \mathrm{~s}$ and $1 \mathrm{~s}$ ?

$\left(\begin{array}{c}12 \\6\end{array}\right)=924$

What is strings ?

The C programming language includes a set of functions executing operations on strings in its standard library. Different operations, such as copying, concatenation, tokenization, and searching are supported.

In C programming, a string exists as a sequence of characters terminated with a null character \0. For example char c[] = "c string"; When the compiler discovers a sequence of characters enclosed in the double quotation marks, it appends a null character \0 at the end by default. The C language does not have a distinctive "String" data type, the way some other languages such as C++ and Java do. Instead, C stores strings of characters as arrays of chars, completed by a null byte.

1. Exactly three 1 s?

$\left(\begin{array}{c}12 \\3\end{array}\right)=220$

2. At most three$1 \mathrm{~s}$ ?

$\left(\begin{array}{c}12 \\0\end{array}\right)+\left(\begin{array}{c}12 \\1\end{array}\right)+\left(\begin{array}{c}12 \\2\end{array}\right)+\left(\begin{array}{c}12 \\3\end{array}\right)=1+12+66+220=299 \text {. }$

3. At least three 1 s?

Take a shortcut by using the previous answer:$2^{12}-66-12-1=4017$

4. An equal number of$0 \mathrm{~s}$ and $1 \mathrm{~s}$ ?

$\left(\begin{array}{c}12 \\6\end{array}\right)=924$

To learn more about strings refer to:

brainly.com/question/27251062

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