Acme Corporation has released an alphabet soup in which each of the vowels (A, E, I, O, U) of the English alphabet appears five times (and the consonants do not appear at all). How many five-letter words can be formed from a bowl of Acme Vowel Soup? (Note: The words do not have to be actual words in English!)

 Jan 16, 2018
edited by SmartMathMan  Jan 17, 2018

well, since there are 5 of each letter and only five letters in a five letter word, then you could do five a's or five u's which is very useful. let us begin.


for the first letter there are 5 different letters to choose from and 1 letter in the word. this makes 5*1=5 1 letter words.


for two letters there is 5 letters for the first letter and another five for the second letter so that makes 5*5=25 2 letter words.


carry on until you get to five letters, where you get 5*5*5*5*5 or 5^5 different words which equals 3125 different five letter words.


so there you have it. there are 3125 different words in you could with five letters in your alphabet soup that only contains vowels for some silly hypothetical reason. peace. cool

 Jan 17, 2018

Thx so much i have needed help on this for a while this was very helpful and i an extremely thankful. THANK YOU!!!

SmartMathMan  Jan 18, 2018

24 Online Users