Combination question...

[sfoksn]

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Carla is having a dinner and inviting 3 boys and 2 girls. Carla must sit at the head of the table, and wants to arrange sitting in a way that no person would sit next to another person of same gender. How many ways can you arrange this?

a. 6
b. 12
c. 24
d. 60
e. 120

Thank you

 

[Streetwolf]

Well it would have to go B-G-B-G-B-G and Carla is stuck at the head of the table.


.........BOY---GIRL
Carla---(TABLE)---BOY
.........BOY---GIRL

So there are 3 places the boys can be. If you had to seat them you could choose 3 for the first seat, 2 for the second, and 1 for the last = 6 ways.

To seat the 2 girls you have 2 for the first seat and 1 for the second = 2 ways.

Together that's 6 x 2 = 12 ways.

I'm just assuming that there's one head of the table and that Carla can't sit on the opposite side where that boy is at.

 

[Mr Dental]

Just to add...
This is a permutation, not a combination question😀

 

[sfoksn]

Thank you!