MHB How many ways can equal number of men and women line up for a photo?

[find_the_fun]

In how many ways can a non-empty collection of people to be chosen from 4 men and 3 women to lineup for a photo if the number of men must be the same as the number of women?

I said

[math]{4 \choose 1} {3 \choose 1} 2! +{4 \choose 2} {3 \choose 2} 4! + {4 \choose 3} {3 \choose 3} 6![/math]

Is this right?

 

[caffeinemachine]

In how many ways can a non-empty collection of people to be chosen from 4 men and 3 women to lineup for a photo if the number of men must be the same as the number of women?

I said

[math]{4 \choose 1} {3 \choose 1} 2! +{4 \choose 2} {3 \choose 2} 4! + {4 \choose 3} {3 \choose 3} 6![/math]

Is this right?

Yes.