LCKurtz said:Your binomial coefficients give the number of ways of choosing 5 women and 5 men. Now you have to figure out how many different pairs you can make with them.
joshmccraney said:how many different pairs...this seems tough. well, I'm thinking of 5 positions. first, for the men there are ##5!## different ways to seat them. now for the women, there are also ##5!## ways to sit them. i think the answer is now ##5!+5!##. however, since women/man is the same as man/women, we divide by ##2!##?
is this correct?
thanks!
The number of possible pairings can be calculated using the combination formula, which is nCr = n! / (r! * (n-r)!). In this case, n = 22 (10 women + 12 men) and r = 2 (since we are pairing 2 individuals at a time). Therefore, the number of possible pairings is 22C2 = 22! / (2! * (22-2)!) = 231 possible pairings.
No, in this scenario, each person can only be paired with one partner at a time. This is because we are considering pairings as exclusive and not allowing for repetition.
In a combination problem, the order of the elements does not matter. For example, pairing person A with person B is considered the same pairing as pairing person B with person A. In a permutation problem, the order does matter. So, pairing person A with person B would be considered a different pairing from pairing person B with person A.
Yes, the number of pairings will change depending on the number of men and women. The number of possible pairings is directly dependent on the total number of individuals in the group.
This type of problem can be applied in situations where we need to consider all possible combinations of a group of people. For example, it can be used in speed dating events where organizers need to consider all possible pairings of men and women. It can also be used in creating seating arrangements for events or assigning group projects in a class.