The number of words, with or without meaning, that can be formed by taking letters at a time from the letters of the word ’SYLLABUS’ such that two letters are distinct and two letters are alike, is
Find the number of words that satisfy the given arrangement conditions
The word SYLLABUS has the following letters,
SS,Y,LL,A,B,U. (Five different letters, two repeated twice)
We need letter words with similar and dissimilar letters.
The two similar letters can be chosen in ways.
The two dissimilar letters can be chosen in ways.
Now the four letters can be arranged in ways.
Hence, the total number of words satisfying the given arrangement
Hence, four letter words are formed such that two of the letters are alike and two are different.