10 gentlemen and 6 ladies are to sit for a dinner at a roundtable the probability that no two ladies sit together is
Answers
The total number of outcomes of n people sitting around the round-table is (n-1)!. This is because for the first person to sit by the round-table has no combination as each and every seat of a round-table are similar. Afrer the first person sits, the other sit becomes unique (example: seat by the first person, seat by the next to next of first person, etc. In this way the sears become unique).
For the required combination, let the 9 gentlemen first stand side by side with a combination of 9!. Along with the last two ends of the gentlemen queue, there is 10 gaps (8 in between and the two ends). Among thise 10 gaps, 6 ladies would get in. The permutations is 10P6. After the required permutations and combinations the ladies and gentlemen would take seats according to the queue by the first gentleman. So, the required outcome is 9!×10P6
The probability is 9!×10P6÷15!