sorry another perms and combs question. probably more to come lmao. (1 Viewer)

[yashbb]

four boys and four girls are arranged in a circle. in how many ways can they be arranged if a particular boy and girl wish to sit next to each other.

 

[B1andB2]

way to rearrange these 2 particular kids is 2!

then rearrange the circle which includes 6 other boys and girls and this block, giving (7-1)!

so multiply them 2! x (7-1)!

 

[yashbb]

thank you!

 

[CM_Tutor]

Looked at another way:

At an empty round table, all positions are the same, so there is only 1 way to seat (arbitrarily) the boy first.

For the girl to be next to him, she must sit in one of the two seats adjacent to him, so in 2 ways.

There are 6 seats remaining and the 6 remaining people can be placed into them in 6! ways.

Hence, number of arrangements with them together is 2 x 6!