Find the number of ways of arranging 6 women and 3 men to stand in a row so that all 6 women are standing together?

Question

Find the number of ways of arranging 6 women and 3 men to stand in a row so that all 6 women are standing together?

Total ways are 17280 I need explaination how?

Answer 1

Since the 6 women are standing together, we can treat them as one group. So now, we have 4 groups of people, and the number of ways to arrange them would be $4!$. However, note that within the 6 women, they are also arranged, so there would be $6!$ ways of arranging the women. So our answer would be $4!*6!=17280$ ways.

Answer 2

Consider 6 women as one unit. So including 3 men we have 4 units.

We can arrange the 4 units in 4! ways.

The women can be arranged within themselves in 6! ways.

So the total number of ways would be 4!*6! = 17280.