### How many 5 letters can be formed out of the letters of the word mathematics of repetition is not allowed?

There are eight (8) different letters in that word, so that's the number of letter choices you have in each 5-letter group without repetition. The number of different 5-letter "words" is (8 x 7 x 6 x 5 x 4) = 6,720 . (They don't necessarily mean anything. They're just distinct sequences of 5-letters each, like Morse-code random practice groups.)