Final answer:
The number of strings of eight uppercase English letters is calculated by raising the number of letter options (26) to the power of the string's length (8). Using the combinatorial rule of product, this gives us a total of 26⁸, which is the correct answer, option (a).
Step-by-step explanation:
The question asks how many strings of eight uppercase English letters there are. This is a problem in combinatorics, a branch of mathematics concerning the study of counting. In this situation, we consider each of the 8 positions in the string, and for each position, there are 26 possible uppercase English letters that could appear there.
To find the total number of different strings, we use the rule of product which states that if there are n ways to do one thing, and m ways to do another thing after the first has been done, then there are n × m ways to do both in sequence. Therefore, for string position 1, there are 26 possibilities, and for string position 2, there are also 26 possibilities, and so on for each of the eight positions. This gives us 26 × 26 × 26 × 26 × 26 × 26 × 26 × 26, or 26 to the power of 8 (26⁸) different combinations.
This form of calculation accounts for all possible variations and permutations of eight-letter strings using the 26 uppercase English alphabet, without any restrictions on repetition of letters. Hence, the correct option is (a) 26⁸.