Olympiad workbook
- Exam
- Olympiad workbook
- Subject
- IOQM
- Chapter
- Permutation and Combination
Olympiad workbook · IOQM · Permutation and Combination
We will say that a rearrangement of the letters of a word has no...
We will say that a rearrangement of the letters of a word has no fixed letters if. When the rearrangement is placed directly below the word, no column has the same letter repeated. For instance, HBRATA is a rearrangement with no fixed letters of BHARAT. How many distinguishable rearrangement with no fixed letters does BHARAThave? (The two A's are considered identical)
Correct answer
84
Step-by-step solution
Let use assume the 's to and
Number of rearrangements of these 6.
=\left\lfloor 6\left(\frac{1}{\lfloor 2}-\frac{1}{\lfloor 3}+\frac{1}{\lfloor 4}-\frac{1}{\lfloor 5}+\frac{1}{\lfloor 6}\right)=265\right.
Let be the set when occupies place of and be the set when occupies place of
Hence required arrangements