Question

How many strings are there over the alphabet {0, 1, 2, 3} whose length is at least 8 and at most 11?

a. 4,194,304
b. 262,144
c. 16,384
d. 1,024

Answer 1

The total number of strings over the given alphabet with a length between 8 and 11 is 5,570,560.

Step-by-step explanation:

To calculate the number of strings over the alphabet {0, 1, 2, 3} with a length between 8 and 11, we need to count the number of possibilities for each length.

For a length of 8, there are 4 choices for each position, so there are 4^8 = 65,536 possibilities.

For a length of 9, there are also 4 choices for each position, so there are 4^9 = 262,144 possibilities.

For a length of 10, there are 4 choices for each position, so there are 4^10 = 1,048,576 possibilities.

For a length of 11, there are 4 choices for each position, so there are 4^11 = 4,194,304 possibilities.

Therefore, the total number of strings is 65,536 + 262,144 + 1,048,576 + 4,194,304 = 5,570,560.