A total of 2 films, 4 different music videos, and 5 different documentaries’ DVDs are to be arranged in a row on a shelf. The number of arrangements in which two film DVDs are together is 9×10!Question 3Select one:TrueFalse
Question
A total of 2 films, 4 different music videos, and 5 different documentaries’ DVDs are to be arranged in a row on a shelf. The number of arrangements in which two film DVDs are together is 9×10!Question 3Select one:TrueFalse
Solution
The statement is False.
To determine the number of arrangements in which two film DVDs are together, we can treat the two film DVDs as a single entity. This means we have a total of 1 film entity, 4 different music videos, and 5 different documentaries' DVDs to arrange.
The total number of entities to arrange is 1 + 4 + 5 = 10.
The number of arrangements of these entities can be calculated using the factorial function. Therefore, the number of arrangements is 10!.
So, the correct statement should be: "The number of arrangements in which two film DVDs are together is 10!"
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