Answer to Question #146447 in Combinatorics | Number Theory for Josh

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!=24"

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


"2!=2"


First operation (the number of permutations of 4 couples) can be result in "n_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 "n_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 "n_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 "n_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 "n_5=2" different ways.

The sequence of five operations can be performed in "24\\cdot2\\cdot2\\cdot2\\cdot2=384" ways.


a.384



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