Probability-3

well, first of all we need to calculate how many ways we can pick 3 men from 10 men and 3 women from 10 women so that'll be $\dbinom{10}{3}$ $\dbinom{10}{3}$ = $14400$ but because 1 man and 1 woman refused to serve together, we can't get them in the calculation ! so let's say that 1 slot have been filled with this 2 guys, so we have 9 men and 9 women left. then we have $\dbinom{9}{2}$ $\dbinom{9}{2}$ = $1296$ So, for the ways to rearrange them without having these 2 guys serving together are $14400$ $-$ $1296$ $=$ $13104$