1. **Problem statement:** Find the number of permutations of the letters A, B, C, D, E, F, G, H that contain: (a) the string "ED" as a block. (b) the string "CDE" as a block. 2. **Formula and rules:** - The total number of permutations of 8 distinct letters is $8!$. - When certain letters must appear together as a block, treat that block as a single element. - Then, find permutations of the reduced set. 3. **Part (a): the string "ED" as a block** - Treat "ED" as one block, so the elements to permute are: {"ED", A, B, C, F, G, H}. - Number of elements now is 7. - Number of permutations is $7!$. 4. **Part (b): the string "CDE" as a block** - Treat "CDE" as one block, so the elements to permute are: {"CDE", A, B, F, G, H}. - Number of elements now is 6. - Number of permutations is $6!$. 5. **Final answers:** - (a) Number of permutations containing "ED" as a block is $$7! = 5040$$. - (b) Number of permutations containing "CDE" as a block is $$6! = 720$$.