# Probability of a problem with a bride and a groom

A group of 7 people including a bride and a groom is to be photographed. In how many ways can you arrange them in 2 rows where one row is a level higher than the other such that the bride and the groom are always in the same row?

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Is this homework? – Pragabhava Nov 24 '12 at 16:19

If the couple is in the top row, we select $k$ guests, $1\le k\le 5$ for the bottom row, arrange the bottom row in one of $k!$ ways, the top row in one of $(7-k)!$ ways, which gives $$\sum_{k=1}^5 k!(7-k)!=1!\cdot6!+2!\cdot5!+3!\cdot4!+4!\cdot3!+5!\cdot2!$$ ways. Double this number to also allow the couple in the lower row.