A group of 6 friends is going to sit in a row for a photo. However, two particular friends insist on sitting together. In how many different ways can they be arranged if they sit together, but not necessarily next to each other?
120
240
420
320
To calculate the number of different ways the group of 6 friends can be arranged in a row for a photo, with two particular friends sitting together but not necessarily next to each other, we can treat the pair of friends as a single entity.
Now, we have 5 entities to arrange: the pair of friends and the remaining 4 individuals.
The number of ways to arrange these 5 entities in a row is 5 !.
However, within the pair of friends, the friends themselves can be arranged among themselves. Since there are 2 friends, the number of ways to arrange them is 2 !.
Therefore, the total number of different ways to arrange the group of 6 friends, with the two particular friends sitting together but not necessarily next to each other, is:
Therefore, there are 240 different ways the group of 6 friends can be arranged in a row for a photo, with the two particular friends sitting together but not necessarily next to each other.
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