a) In how many different ways can the letters of the word "CORPORATION" be arranged so that the vowels always come together? b) In how many different ways can the letters of the word "DETAIL" be...

Extracted text: a) In how many different ways can the letters of the word "CORPORATION" be arranged so that the vowels always come together? b) In how many different ways can the letters of the word "DETAIL" be arranged such that the vowels must occupy only the odd positions? c) How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5, and none of the digits is repeated? d) In how many ways can you divide 28 persons into three groups having 4, 12 and 12 persons?