TS EAMCET · Maths · Permutation Combination
If 3 sisters and 8 other girls are together playing a game, then the number of ways in which all the girls are seated around a circle such that the three sisters are not seated together, is
- A \(11 ! \times 8\)
- B \(8 ! \times 504\)
- C \(7 ! \times 210\)
- D \(8 ! \times 84\)
Answer & Solution
Correct Answer
(D) \(8 ! \times 84\)
Step-by-step Solution
Detailed explanation
The total number of ways that all girls seated around a circle is 10 !. The number of ways the three sisters seated together along with the other girls is \(8 ! \times 3\) !. So, required number of ways \(= 10 !-8 ! 3 !\) \(=8 !(10 \times 9-6)\) \(=8 ! \times 84\)
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