Calculate the followings with proper explanation:

(a) How many arrangements are possible from the letters as in WE PLAY CHESS AT HOME, placing vowels at the first and last position?

(b) Given the sets P, Q have 15 alphabets, 10 digits, respectively. As a lab administrator of CSE at NSU, you are asked to generate passwords. Each password you generate is six to eight characters long, and the 1 password must contain at least one digit in it. How many passwords can you generate using the given sets P and Q?

DO IT BY PERMUTATION AND COMBINATION