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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.

 Jun 29, 2020
 #1
avatar+26007 
+1

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)

 Jun 29, 2020
 #2
avatar+302 
+1

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

 Jun 29, 2020

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