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

Question

anonymous · Answer

@ganeshie8 @ParthKohli @AriPotta

parthkohli · Answer

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.

parthkohli · Answer

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

anonymous · Answer

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

anonymous · Answer

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

parthkohli · Answer

Just like you did the last time.

parthkohli · Answer

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

anonymous · Answer

See I messed up somewhere I got 5028...

ganeshie8 · Answer

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

anonymous · Answer

720
4,320
3,600
4,000

parthkohli · Answer

Why 5C3?

parthkohli · Answer

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

ganeshie8 · Answer

place girls in the blanks first
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parthkohli · Answer

Oh, I see.

ganeshie8 · Answer

after that, we have 5 places for placing boys 

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