In how many ways can 3 men and 3 women sit in a row such that no two men or women sit adjacent to each other.
+37146 m w m w m w
or
w m w m w m within the group of 3 men there are 6 ways to arrange them.....same for the women ...in the two arrangements listed here
6 x 6 x 2 = 72 ways (I think)
+310 Anyone can sit in the first seat so there are 6 choices.
For the second seat there are 3 choices- the opposite gender of the person in the first seat.
For the third seat, there are 2 choices- the other two people of the same gender as the person in the first seat.
For the fourth seat, there are 2 choices- the other two people of the same gender as the person in the second seat.
For the fifth seat, there is 1 choice left- the same gender as the first and third seat.
For the sixth seat, there is 1 choice left- the same gender as the second and fourth seat.
So 6*3*2*2*1*1=72
