Question

The number of ways of dividing $2n$ people into $n$ couples is

• A. $\frac{2n!}{2^{n-1}n!}$
• B. $\frac{2n-1!}{2^n!}$
• C. $\frac{2n!}{2^{n}n!}$
• D. None of these

Answer 1

The correct option is C $\frac{2n!}{2^{n}n!}$

Number of ways of dividing these people ${=}^{2n}{P}_n=\frac{2n!}{n!}$
There are $2^n$ similar people(as they are couples)
So total $=\frac{2n!}{2^n.n!}$
Hence, option 'C' is correct.