Final answer:
The number of ways to arrange 10 women and six men in a line with no two men next to each other is the factorial of the number of women multiplied by the combination of possible spaces for men and the factorial of the number of men, which is 10! * C(11, 6) * 6!.
Step-by-step explanation:
To find the number of ways 10 women and six men can stand in a line so that no two men stand next to each other, we first arrange the women, since they have no restrictions. There are 10! ways to arrange the 10 women.
Next, for the men to not stand next to each other, they must be placed in the spaces between the women. There are 11 possible spaces where the men can be placed (one before the first woman, nine between each pair of women, and one after the last woman).
We need to choose six of these 11 spaces for the men, which can be done in C(11, 6) ways, where C denotes the combination function. Each arrangement of the six men can be done in 6! ways.
Therefore, the total number of arrangements is the product of the number of ways to arrange the women, the combinations of spaces, and the arrangements of the men.
The final calculation is 10! * C(11, 6) * 6!.