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

Question

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

TestHub · Accepted Answer

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

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