EXTRATERRESTRIAL a) How many anagrams of the word are there if all the vowels ar

Question

        EXTRATERRESTRIAL         
a) How many anagrams of the word are there if all the vowels are together?

b) How many anagrams are there if all the vowels are together and in alphabetical order?

        c) How many anagrams are there if all the vowels are in alphabetical order?

        d) How many anagrams are there if all the vowels are in alphabetical order and all the consonants are in alphabetical order too?

        e) How many anagrams are there if all the vowels are together and inalphabetical order, and so are the consonants?

        f) How many anagrams are there if all the letters are in alphabetical order?

        EXTRATERRESTRIAL         
a) How many anagrams of the word are there if all the vowels are together?

b) How many anagrams are there if all the vowels are together and in alphabetical order?

        c) How many anagrams are there if all the vowels are in alphabetical order?

        d) How many anagrams are there if all the vowels are in alphabetical order and all the consonants are in alphabetical order too?

        e) How many anagrams are there if all the vowels are together and inalphabetical order, and so are the consonants?

        f) How many anagrams are there if all the letters are in alphabetical order?

Explanation / Answer

(a)no. of anagrams = 11!6!/(3!4!3!2!)

(b)no. of anagrams = 11!/(3!4!)

(c)no. of anagrams = 16!2!3!/(2!3!3!4!6!) = 16!/(3!4!6!)

(d)no. of anagrams = 16!/(6!10!)

(e)no. of anagrams = 2!

(f)no. of anagrams = 1

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