[Math] Permutation-Arranging Bride and Groom

discrete mathematics

In how many ways can a photographer at a wedding arrange six people in a row, including the bride and groom, if the bride is positioned somewhere to the left of the groom?


Assuming the bride is at the furthest to the left spot:

Why is the first line 5!

Assuming she's at the 2nd spot:

Why is it $4*4!$

If someone could explain that would be appreciated

Best Answer

The easiest way to solve this is to observe that there are $6!=720$ permutations of the $6$ people. In half of these, the bride is to the right of the groom, and in half of them, the bride is to the left of the groom.

So the answer is $\dfrac{6!}{2}=360.$