Need some help with this question…
At a party $6$ boys and $6$ girls dance together. Assuming that the classical dance is performed, in which one couple (one boy and one girl), how many couples can perform together?
I know the answer is $6!$ because you take just one group (boys or girls) to assess but I don't understand the logic behind it. If someone could enlighten me I'll be very grateful.
Best Answer
To give an intuitive angle to the problem, imagine that a single boy can dance with any of the 6 girls. When this happens, the next boy can dance with any of the 5 remaining girls, the next boy any of the 4 remaining girls, and so on, so we have the following ways of arranging the dance partners:
$$6\times 5 \times 4 \times 3 \times 2 \times 1 = 6!$$
This is how we get $6!$ as our answer. I hope this helps you to understand, if you still have questions, feel free to comment and I will do my best to answer them.