The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is

Step-by-step solution

From the given word, S - 2 , L - 2 , A , B , Y , U . Number of alike letter pairs = 2 Number of ways to select one pair = C 1 2 Number of distinct letters = 5 Number of ways to select two distinct letters = C 2 5 Number of ways to arrange four letters if two are alike = 4 ! 2 ! Required number of ways = C 1 2 C 2 5 · 4 ! 2 ! = 2 · 10 · 24 2 = 240