Artificial intelligent assistant

problem with permutation In how many ways can the letters of the word "ALPHABET" be arranged , if vowels are retain to their places , if consonants are retain to their places?

> In how many ways can the letters of the word "ALPHABET" be arranged , if vowels are retain to their places , if consonants are retain to their places?

How many ways are there to arrange the vowels, $\rm AAE$ among their places?

How many ways are there to arrange the consonants, $\rm LPHBT$ among their places?

How many ways are there to do both these tasks in series?

xcX3v84RxoQ-4GxG32940ukFUIEgYdPy 7eac6ef5f2121259c7aabc775153550c