Final answer:
The number of two-letter combinations that can be made using the letters in the word "humble" is calculated using the combination formula C(n, k) = n! / (k!(n-k)!), which results in 15 different combinations.
option b is correct answer.
Step-by-step explanation:
The question asks how many two-letter combinations can be made using the letters in the word "humble". This is a problem of combinatorics, specifically combinations without repetition because the order of selection does not matter, and each letter can only be used once in each combination.
To calculate the number of combinations, we use the formula for combinations without repetition which is C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, and k is the number of items to choose. In this case, n is 6 (since "humble" has 6 different letters), and k is 2 (since we are creating two-letter combinations).
Therefore, the number of combinations: C(6, 2) = 6! / (2!(6-2)!) = (6×5) / (2×1) = 30 / 2 = 15.
So, the correct answer is b. 15.