How many ways are there to pick a man and a woman from

[Guest]

I'm having issues with this problem, can anyone help me?

How many ways are there to pick a man and a woman who are not husband and wife from a group of n married couples?

 

[arthur ohlsten]

break the group up into two sets:
N men and N woman

choose a man , any of n
AND
choose a woman , any of n-1

[1Cn][1C(n-1)] = n!/{1![n-1]!} times {[n-1]!/1![n-2]!}
n[n-1] answer

Arthur

 

[pka]

Assuming that having n couples then we can identify n husbands and n wives.
That is 2n people.
Now surely we can choose a wife first in \(\displaystyle n \choose 1\) ways. Then we need to choose a non-partner from the non-matched husbands, \(\displaystyle \left( {\begin{array}{c}
{n - 1} \\
1 \\
\end{array}} \right)\)