There are 10 men and 10 women. Alice (woman) and Brad (man) never stand next to each other. Assume that the men and women alternate in a line, how many possible ways are there for the arrangement?
Without the condition of Alice and Bob not standing next to eachother, it would be 10! * 10! * 2. Now I need to subtract all the ways in which they could be stuck together, or 9! * 9! * 10 * 2. (I can elaborate on how I got this part if it is wrong)
So would the final answer just be 10!10!2 - 9!9!10*2 ??