Question #146447
In how many ways can 4 married couples attending a concert be seated in a row of eight seats if each couple must be seated together?
a.384
b.192
c.129
d.16
1
Expert's answer
2020-11-29T19:24:52-0500

Let's observe one couple (two persons) as one object. Now we have 4 objects (couples). The number of permutations of 4 objects is


4!=244!=24

Each couple consists of 2 persons. The number of permutations of 2 persons in each couple is


2!=22!=2


First operation (the number of permutations of 4 couples) can be result in n1=24n_1=24 different ways.

Then for each of these ways a second operation (the number of permutations of persons in first couple) can be performed in n2=2n_2=2 different ways.

For each of these ways a third operation (the number of permutations of persons in second couple) can be performed in n3=2n_3=2 different ways.

For each of these ways a fourth operation (the number of permutations of persons in third couple) can be performed in n4=2n_4=2 different ways.

For each of these ways a fifth operation (the number of permutations of persons in fourth couple) can be performed in n5=2n_5=2 different ways.

The sequence of five operations can be performed in 242222=38424\cdot2\cdot2\cdot2\cdot2=384 ways.


a.384



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