- #1
diceyfume
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How many six-letter words (not necessarily with sense) composed of 4 different consonants and 2 different vowels can be formed from the English Alphabet?
The total number of six-letter words that can be composed of 4 different letters is 840.
Yes, the formula is nPr = n! / (n-r)! where n is the number of available letters and r is the length of the word. In this case, n = 4 and r = 6, so the formula becomes 4P6 = 4! / (4-6)! = 4! / (-2)! = 4*3*2*1 / 1 = 24 / 1 = 24. However, this formula does not take into account repeated letters or the sense of the words.
Yes, repeated letters can be included in these words. However, this will increase the total number of possible words. For example, if we allow repeated letters, the word "apple" can be composed as "applle" as well, resulting in two different words.
The difference is that in the former, only 4 distinct letters are used in each word, while in the latter, any 4 letters can be used, including repeated letters. This means that the total number of words in the latter case will be higher than the former.
The sense or meaning of the words does not affect the total number of possible words. As long as the words are composed of 4 different letters and are 6 letters in length, they will be part of the total count of 840 possible words. However, the sense or meaning of the words may affect the number of actual words that are recognized in a language.