In how many ways can six boys and five girls stand in line so that no two girls are next to each other ?

Question

In how many ways can six boys and five girls stand in line so that no two girls are next to each other ?

Answer 1

I have found 1 way...
boy
girl
boy
girl
boy
girl
boy
girl
boy
girl
boy

Answer 2

We can arrange them strictly alternating one way.
B G B G B G B G B G B

We can arrange them with two boys next to each other in one place ten ways.
B B G B G B G B G B G
B G B B G B G B G B G
B G B G B B G B G B G
B G B G B G B B G B G
B G B G B G B G B B G

G B B G B G B G B G B
G B G B B G B G B G B
G B G B G B B G B G B
G B G B G B G B B G B
G B G B G B G B G B B

We can arrange them with two boys next to each other in two places six ways.
G B B G B B G B G B G
G B B G B G B B G B G
G B B G B G B G B B G
G B G B B G B B G B G
G B G B B G B G B B G
G B G B G B B G B B G

We can arrange them with three boys next to each other four ways.
G B B B G B G B G B G
G B G B B B G B G B G
G B G B G B B B G B G
G B G B G B G B B B G

This is a total of 1 + 10 + 6 + 4 = 21 arrangements.

Answer 3

In how many ways can six boys and five girls stand in line so that no two girls are next to each other ?

Answer 4

B G B G B G B G B G B
This is one way.
You could also take the last B and put him in front
B B G B G B G B G B G
So now 2 boys are together.
You can see that there are 6 ways to put 2 boys together like that. Just change the position.
B G B B G B G B G B G
etc etc
Now you can also put 3 boys together.
G B B B G B G B G B G
There are 4 ways this can happen.

You cannot put 4 boys together.

So in total there are 11 ways.

Answer 5

There's a lot of possible ways to do this.

representation: b-boy and g-girl

1: b-g-b-g-b-g-b-g-b-g-b (alternate)

then the other ways are basically the same,

2: b-b-g-b-g-b-g-b-g-b-g
3: b-g-b-b-g-b-g-b-g-b-g
4: b-g-b-g-b-b-g-b-g-b-g
5: b-g-b-g-b-g-b-b-g-b-g
6: b-g-b-g-b-g-b-g-b-b-g

7: g-b-b-g-b-g-b-g-b-g-b
8: g-b-g-b-b-g-b-g-b-g-b
9: g-b-g-b-g-b-b-g-b-g-b
10: g-b-g-b-g-b-g-b-b-g-b
11: g-b-g-b-g-b-g-b-g-b-b


12: g-b-b-b-g-b-g-b-g-b-g
13: g-b-g-b-b-b-g-b-g-b-g
14: g-b-g-b-g-b-b-b-g-b-g
15: g-b-g-b-g-b-g-b-b-b-g

i guess there are 15 possible ways to arrange them.

Answer 6

Do you 'like' your husband?

Answer 7

He's mainly as not sure as you're, both he isn't calling in view that he obtained what he desired out of the deal or he isn't calling in view that he does not wish to appear obsessive. Try to not force your self loopy with this, and busy your self with different matters at the same time you wait to listen to from him. Don't get clingy and obsessive now in view that so as to force him to this point away, if you do not listen from him inside the week.. I feel you can be out of success.

Answer 8

The arrangement will be:
B G B G B G B G B G B

number of ways
= 6! * 5!
= 720 * 120
= 86400

Answer 9

What types of girls intimidate guys most?