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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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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

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