Question

In Morse code, symbols are represented by variable-length sequences of dots and dashes. (For example, A =:-, 1=-----/?="--) How many different symbols can be represented by sequences of eight or fewer dots and dashes? Use the method of Example 9.5.10 to answer the following questions. (a) How many 18-bit strings contain exactly eight 1's? The number of 18-bit strings that contain exactly eight 1's equals the number of ways to choose the positions for the l's in the string, namely, (b) How many 18-bit strings contain at least fifteen l's? (c) How many 18-bit strings contain at least one 17 (d) How many 18-bit strings contain at most one 1?

Answer 1

Applying the product rule of exponents, (a²c)³ = .

What is the Product Rule of Exponents?

When multiplying two numbers with the same base, their powers/exponents would be added.

For example, .

Given:

(a²c)³

Therefore:

(a²c)³ = (a²c)(a²c)(a²c)

(a²c)³ =

(a²c)³ =

Therefore, applying the product rule of exponents, (a²c)³ = .

Explanation: