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

#### find_the_fun

##### Active member
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

$$\displaystyle {4 \choose 1} {3 \choose 1} 2! +{4 \choose 2} {3 \choose 2} 4! + {4 \choose 3} {3 \choose 3} 6!$$

Is this right?

#### caffeinemachine

##### Well-known member
MHB Math Scholar
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

$$\displaystyle {4 \choose 1} {3 \choose 1} 2! +{4 \choose 2} {3 \choose 2} 4! + {4 \choose 3} {3 \choose 3} 6!$$

Is this right?
Yes.