At a wedding reception, the bride and groom and five attendants will form a receiving line. How many ways can they be arranged in each of following cases? a) Any order will do. b) The bride and groom must be the last two in line. c) The groom must be last in line with the bride next to him.

Question

Landin

Mathematics

25 May, 18:24

At a wedding reception, the bride and groom and five attendants will form a receiving line. How many ways can they be arranged in each of following cases? a) Any order will do. b) The bride and groom must be the last two in line. c) The groom must be last in line with the bride next to him.

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Alisa Atkins · Answer 1

A. In this case, they can be arranged at any order. Since there are 7 people all in all, therefore the number of arrangements is:

number of arrangements = 7P7 = 5040 ways

B. In this case, only the 5 people can be arranged in any order therefore 5P5. However the groom and bride can be interchanged on 2 places, therefore:

number of arrangements = 5P5 * 2 = 240 ways

C. In this case, only the 5 people can be arranged in any order while the groom and bride can no longer be interchanged, therefore:

number of arrangements = 5P5 = 120 ways