6 men and 4 women are to be seated in $a$ row so that no two women sit together. The number of ways they can be seated is ________.

Step 1 (Arrange the Men): First, we seat the 6 men in a row. The number of ways to arrange 6 distinct men is:

Step 2 (Identify Gaps for Women): To ensure no two women sit together, we place the 4 women in the gaps between the men (and at the ends). For 6 men seated in a row:

There are exactly $6+1=7$ available gaps/slots.

Step 3 (Arrange the Women in Gaps): We choose 4 distinct gaps out of 7 for the 4 women and arrange them. The number of ways is given by permutations $P(7,4)$:

Step 4 (Multiply the Permutations): Total ways = (Ways to arrange men) $\times$ (Ways to place women):

Step 5 (Conclusion): The number of seating arrangements is exactly 604800.