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  • A group of 15 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?</

A group of 15 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?

 

Option: 1

10 ! / 2 !


Option: 2

12 ! / 2 !


Option: 3

14 ! / 2 !


Option: 4

15 ! / 2 !


Answers (1)

best_answer

To calculate the number of different ways the group of 15 friends can be arranged, with two particular friends sitting together, we can consider those two friends as a single entity. This reduces the problem to arranging 14 entities (13 individuals +1 pair of friends) in a row.

Now, we can treat the pair of friends as a single entity, which means we have 14+1=15 entities to arrange. The number of different arrangements of these entities is given by 15 !.

However, within these arrangements, the two friends can also swap places among themselves, which means we need to divide the total number of arrangements by 2 !.

Therefore, the number of different ways the group of 15 friends can be arranged, with the two particular friends sitting together, is:

\mathrm{ 15 ! / 2 !=1,307,674,368,000 / 2=653,837,184,000 . }

Therefore, there are 653,837,184,000 different ways the group of 15 friends can be arranged with the two particular friends sitting together.

Posted by

Gautam harsolia

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