## anonymous one year ago In how many arrangements can 3 boys and 4 girls stand in a row such that no two boys are together?

1. anonymous

@ganeshie8 @ParthKohli @AriPotta

2. ParthKohli

Number of ways that they can stand in - number of ways two boys can stand together. Note that the latter also covers the number of ways in which three boys can stand together.

3. ParthKohli

Oh, and also keep in mind that they can permute among themselves, like @ganeshie8 spotted the last time.

4. anonymous

I got 5040 at total number of ways they can stand together

5. anonymous

How would you calculate the number of ways two boys can stand together? I feel like I am messing up there

6. ParthKohli

Just like you did the last time.

7. ParthKohli

Oh, and yes, you have three boys, so you also need to see that you can choose any 2 out of 3 boys.

8. anonymous

See I messed up somewhere I got 5028...

9. ganeshie8

4 girls can be arranged in 4! after that, 3 boys can be inserted in between the boys in 5C3 * 3! ways so in total we have 4! * 5C3*3! = 1440 ways

10. anonymous

720 4,320 3,600 4,000

11. ParthKohli

Why 5C3?

12. ParthKohli

$7! - 2 \cdot \binom{3}{2}\cdot 6!$

13. ganeshie8

place girls in the blanks first |dw:1432838542055:dw|

14. ParthKohli

Oh, I see.

15. ganeshie8

after that, we have 5 places for placing boys |dw:1432838582145:dw|

16. anonymous

but 1440 is not an option. so what is wrong?

17. ParthKohli

Is 720 correct? Just wondering...

18. anonymous

720 is an option

19. ParthKohli

Is the option correct?

20. anonymous

I dont think so?

21. ParthKohli

What's the correct one?

22. anonymous

Im not sure :/

23. ganeshie8

i don't see how it cannot be 1440

24. anonymous

1440 is that arrangement is the only the girls are sitting on the end seats

25. anonymous

Pattern: gbgbgbg # of arrangements: 4!*3! = 144

26. ganeshie8

girls need not be in the ends |dw:1432839047302:dw|

27. anonymous

# of ways to fill the end seats: 4*3 = 12 # of ways to fill the other 5 seats: 5! # of arrangements: 12*5! = 1440

28. anonymous

yeah :/ I am getting the same way... but this is not an answer...

29. ganeshie8

as the question stands, 1440 is the correct answer it just so happens that the options don't have the correct answer... inform ur teacher and move on to next q