7 male students and 3 female students sit around a round table. What is the probability that all three female students are sitting side-by-side?
Consider the total (the denominator). For the total (without considering restrictions) there are \(10!/10= (10*9*8...2*1)/10=9!.\) (due to rotational fixations). This is because there are 10 ways that we could rotate the table (so we overcount by a factor of 10).
Numerator case: You should be able to find the ways that the women sit next to each other by considering where to fix the womens' spots then using constructive counting. It may be easier if you use variables. Hint: \(W_1,M_1\).