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

find_the_fun

Active member
Feb 1, 2012
166
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
Mar 10, 2012
834
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.