How many ways are there for 6 men and 4 women to stand in a

How many ways are there for 6 men and 4 women to stand in a line so that no two women stand next to each other (First, determine where the men are standing and then consider the women)

Solution

6 men and 4 women

no two women stand next to each other

Hence first arrange all 6 men in a line

This can be done in 6! ways

Now there will be 7 places for women including two extreme ends

5 women can be placed in 7 places in 7C5 ways

Hence total ways = 6! (7C5)

= 720(21)

= 15120