Question

How many ways are there for 8 men and 5 women to stand in a line so that no two women stand next to each other?

Answer 1

Answer:

609638400

Step-by-step explanation:

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.