Solve the following a How many permutations of all 26 letter

Solve the following:

a. How many permutations of all 26 letters of the alphabet are there that contain at least one of the words: CAR, CART, SCARF, SCARE, SCAR?

b. How many permutations of all 26 letters of the alphabet are there that contain at least one of the words: MAZE, SWORD, PLANT, CARTS?

This computer science but:

a) The answer should be Factorial(24) i.e . factorial of 24. It can be solved by formulating a simple recurrence relation.

b)(26C4+26C5+26C5+26C5)/26!.

It can also be seen as a recurrence relation and solved.