SOLUTION: Five couples (ten people) are standing in line. If the order is completely random, what is the probability that each person will be standing next to his/her spouse?

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Question 260055: Five couples (ten people) are standing in line. If the order is completely random, what is the probability that each person will be standing next to his/her spouse?
Found 2 solutions by edjones, dabanfield:
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
1/5!=1/120

Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website!
Five couples (ten people) are standing in line. If the order is completely random, what is the probability that each person will be standing next to his/her spouse?
The number of choices for the first person in the line is 10. Then for each of these 10 choices there are 9 choices for the second position, 8 for the third and so on. The total number of ways for the 10 "people" (without any regard to couples)to be in the line then is 10*9*8*7*6*5*4*3*2*1 or 10!
Similarly the number of ways for the 5 "couples" to be arranged is 5*4*3*2*1 = 5!. This does not take into account that for each couple there are two ways for them to be arranged (man first, woman second, and woman first, man second).
The total number of arrangements preserving the couples is then 2*5!.
The probability then is 10!/(2*5!).