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In order to advertise the movie E.T., a theater hires 16 children to hold the le

ID: 2968852 • Letter: I

Question

In order to advertise the movie E.T., a theater hires 16 children to hold the letters

of the word EXTRATERRESTRIAL.


?? In how many ways can the children be assigned letters to hold?


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


?? How many anagrams are there if all the vowels are together and in

alphabetical order?


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


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

and all the consonants are in alphabetical order too?


?? How many anagrams are there if all the vowels are together and in

alphabetical order, and so are the consonants?


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

Explanation / Answer

Take out the consonants and you have the letters
_A_E_I_O_U_Y_. The number of words will be the number of ways of arranging the 5 consonants.

When you place the first consonant, you have seven places to put the letter (five between two vowels and two at either end.) After you place the first consonant, you have eight places to put the second consonant ( six between two letters and two at either end) and so forth. The final number of arrangements will be
(7)(8)(9)(10)(11) = 55,440 words.

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