## Precalculus (6th Edition) Blitzer

$14400$ ways.
The first place is a woman and has 5 choices. The second place is a man and has 5 choices. The third place is a woman and has 4 choices. The fourth place is a man and has 4 choices. Thus, the total number is $5\times5\times4\times4\times3\times3\times2\times2\times1\times1=14400$ ways.