Find the number of arrangements of letters in the word MUMBAI so that the letter B is always next to A

The number of arrangements of the letters of the word CALCUTTA is

Find the number of arrangements of the letters in the word SOLAPUR so that consonents and vowels are placed altenatively.

Find the number of arrangements of letters in the word CONSTITUTION that begin and end with N.

Determine the number of arrangements of letters of the word ALGORITHM if. (a) vowels are always together. (b) no vowels are together. (c) consonants are at even positions. (d) O is the first and T is the last letter.