Question 263018
There are 4 men and 4 women.
The top 3 finishes will include exactly one woman.
Out of 8 competitors 3 can be selected in 8C3 = (8*7*6)/(1*2*3) = 56 ways
Out of 4 women 1 can be selected in 4 ways.
Out of 4 men 2 can be selected in 4C2 = (4*3)/(1*2) = 6 ways.
Number of favorable ways = 4*6 = 24
The probability the top 3 finishes will include exactly one woman = 24/56
                                                                  = 3/7