Question

If 2 boys and 2 girls are to be arranged in a row so that the girls are not next to each other, how many possible arrangements are there?

a) 3
b) 6
c) 12
d) 24

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Answer 1

Let boys are B1 , B2 and girls are G1 and G2.

1. B1 , G1 , B2 , G2

2. B2, G1 , B1 , G2

3.  B1 , G2 , B2 , G1

4. B2 , G2 , B1 , G1

5. G1 , B1 , B2 , G2

6. G1 , B2 , B1 , G2

7. G2 , B1 , B2 , G1

8. G2 , B2 , B1 , G1

9. G1 , B1 , G2 , B2

10. G2 , B1 , G1 , B2

11. G2 , B2 , G1 , B1

12. G1 , B2 , G1 , B1.

So , in 12 ways this arrangement can be done.

Answer 2

-G-G-

2 Girls can sit in any of the 2 places in 2P2 ways.

= > 2! ways.

= > 2!/(2 - 2)!

= > 2!/0!

= > 2!

= > 2.




Now,

2 boys can sit in the remaining 3 places in 3P2 ways

= >  3!/(3 - 2)!

= > 3!/(1)!

= > 3!

= > 6.


Therefore the total number of ways = 2 * 6

                                                             = 12.



Hope this helps!