The number of ways in which a committee of 3 ladies and 4 gentleman can be appointed from a meeting consisting of 8 ladies and 7 gentleman, if Mrs  x refuses to serve in  a committee, if Mr. y is its member, is:

In how many rearrangements of the word AMAZED, is the letter ‘E’ positioned in between the 2 ‘A’s (Not necessarily flanked)?

In how many different ways can the letters of the word “AUCTION” be arranged in such a way that the vowels always come together?