In other previous questions alike, some of the answers were: "ANSWER: 609638400. Explanation: We can line up the eight men in P(8,8) ways. This creates nine spaces, seven between successive males and two at the ends of the row.
Hence, we need to find how many ways we can arrange 5 women in the 9 possible (as shown above) places,this is actually 9P5=9∗8∗7∗6∗5=15120
Now applying the fundamental law of counting (precisely product rule), total number of possible arrangements satisfying both constraints is: 15120∗40320=609638400 which is your required/desired answer."
Now,I've got several questions:
Why is it not possible to have just 7 or 8 spaces for women instead of 9: M1 _ M2 _ M3 _ M4 _ M5_ M6 _ M7 _ M8
What about arrengements like:
W1 M1 M2 M3 W2 M4 M5 W3 M6 M7 W4 M7 W5
M1 M2 W1 M3 M4 W2 M5 W3 M6 W4 M7 M8 W5
How can these possibilities be taken into account when 2, 3 or even 4 men could be next to one another and still fulfill the restricions? Or it is logical to assume these problems with alternancy men/women?