A computer dating service wants to match each of four women with one of six men. According to the information these applicants provided when they joined the service, we can draw the following conclusions.
• Woman 1 would not be compatible with man 1, 3, or 6.
• Woman 2 would not be compatible with man 2 or 4.
• Woman 3 would not be compatible with man 3 or 6.
• Woman 4 would not be compatible with man 4 or 5.
In how many ways can the service successfully match each of the four women with a compatible partner?