Final answer:
The number of strings that can be formed by ordering the letters abcde containing the substrings 'db' and 'ae' is 18. This is found by treating the substrings 'db' and 'ae' as single units alongside 'c' and calculating the permutations.
Step-by-step explanation:
To determine how many strings can be formed by ordering the letters abcde with the condition that they contain the substrings db and ae, we can treat each of these substrings as single units. This simplifies the problem because we only need to arrange these units along with the remaining letters.
Let us represent db as X and ae as Y. Now we have three 'letters' to arrange: X, Y, and c. The number of different strings we can form with these three items is 3! (three-factorial), which is 3×2×1 = 6 permutations.
However, within each permutation, the letter 'c' can appear in three different positions since it can be placed before X, between X and Y, or after Y. Since there are 6 permutations for XYZ, and for each permutation, there are 3 possibilities of inserting 'c', we multiply 6 by 3 to get the total number of strings that can be formed, which is 18.
Thus, none of the provided options (a) 4, (b) 8, (c) 12, (d) 16 correctly states the number of strings that can be formed under the given conditions. The correct answer is actually 18.