Permutations and Combinations
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
we have to separate the consonants and vowels and consider each time the set of the consonants and vowels as a single letter.
here, word is E Q U A T I O N
vowels —> E , U, A , I , O ( there are five vowels in given words )
consonants—> T, Q , N ( there are 3 consonants in given words )
the vowels can be arranged in ways
the consonants can be arranged in ways
These vowels and consonants ( when we take as a single letter )can be arranged ways .
hence, a/c to fundamental principle of counting
total number of ways