Please answer with steps.

8. [8 points] How many diiferent strings can be formed that are permutations of the 10-character string abcdefghij and satisfy the following additional restrictions? (a) No additional restrictions. (b) The character a appears immediately before the character b. (c) The characters a and b are next to each other. (d) The character a appears before the character b, but not necessarily immediately before it