7. Recall that the number of ways to arrange n items in a row is n!.
a) Think of the bride and groom as one item, which means there are five items to be arranged. Keep in mind that there are two ways for the bride and groom to stand next to each other.
b) It is easiest to calculate the number of ways for the groom's mother to be next to the bride and then take this number away from the total number of ways to arrange the six people.
c) Consider this in 5 cases. Call the positions (from left to right) positions 1, 2, 3, 4, 5 and 6. Since the bride's mother must be to the left of the groom, the groom could be in position 2, 3, 4, 5 or 6. The first position to fill is the position of the groom, then the positions to the right of the groom (which cannot include the bride's mother, so there are only four choices of people to the right of the groom) and finally the positions to the left of the groom. Work out the number of possibilities for each case individually and then add them all together.