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 \_\_\_\_\_\_\_\_.
Answer: 240
Solutions · 1
Official solution
SYLLABUS: S\times 2, L\times 2, and Y,A,B,U once each.
Choose the repeated letter (S or L): (12)=2. Choose 2 distinct letters from the remaining 5 distinct letter-types: (25)=10. Arrange the 4 letters (with one pair identical): 2!4!=12.
\[\text{Total} = 2\times10\times12 = 240\]