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

In summary, the number of ways that an equal number of men and women can line up for a photo depends on the total number of people in the group and can be calculated using the formula nCr = n! / r!(n-r)!. The order of the men and women does matter in the photo and if there are more men than women or vice versa, it will not be possible to have an equal number of both genders in the photo. However, the men and women can stand in any order they want as long as there is an equal number of both genders. It is possible to calculate the number of ways for a large group of men and women to line up, but it may be difficult to do so manually and a calculator
  • #1
find_the_fun
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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?
 
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  • #2
find_the_fun said:
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.
 

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

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

The number of ways that an equal number of men and women can line up for a photo depends on the total number of people in the group. For example, if there are 4 men and 4 women, there are 35 possible ways they can line up. This can be calculated using the formula nCr = n! / r!(n-r)!, where n is the total number of people and r is the number of men or women.

Does the order of the men and women matter in the photo?

Yes, the order of the men and women does matter in the photo. If the same group of people is arranged in a different order, it will result in a different photo. For example, if there are 3 men and 3 women, there are 20 possible ways they can line up.

What if there are more men than women or vice versa?

If there are more men than women or vice versa, it will not be possible to have an equal number of men and women in the photo. For example, if there are 5 men and 3 women, there will always be 2 men left over without a female partner to stand next to. Therefore, the number of ways they can line up will be 0.

Can the men and women stand in any order they want in the photo?

Yes, the men and women can stand in any order they want in the photo as long as there is an equal number of both genders. However, for the purpose of this question, we are assuming that the men and women are standing in a straight line and not in a specific arrangement or pattern.

Is it possible to calculate the number of ways for a large group of men and women to line up?

Yes, it is possible to calculate the number of ways for a large group of men and women to line up. However, the number can become very large and difficult to calculate manually. In this case, it is best to use a calculator or computer program to determine the total number of ways.

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