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(# of ways 7 children can be arranged around a circular table) - (# of ways the 2 children can be seated together)

# of ways 7 can be arranged in a circular pattern = 6! # of ways 2 can be seated together = 2.5!

# of ways 2 children cannot be seated together in a circular pattern = 6! - 2.5!.

Is this the OA ? Please explain how did you get 2.5!

Thanks

take for example a and b as the two children. they sit in the first and second position. next to them there are 5*4*3*1 possible ways to sit the other children. we multiply by 2 because there are even more ways when a and b switch their seats.

(# of ways 7 children can be arranged around a circular table) - (# of ways the 2 children can be seated together)

# of ways 7 can be arranged in a circular pattern = 6! # of ways 2 can be seated together = 2.5!

# of ways 2 children cannot be seated together in a circular pattern = 6! - 2.5!.

Is this the OA ? Please explain how did you get 2.5!

Thanks

take for example a and b as the two children. they sit in the first and second position. next to them there are 5*4*3*1 possible ways to sit the other children. we multiply by 2 because there are even more ways when a and b switch their seats.

I'M completely lost here.

Let's say we have seats A-G. i.e. A,B,C,D,E,F,G
then, the no. of ways 2 people can stay together is:

(# of ways 7 children can be arranged around a circular table) - (# of ways the 2 children can be seated together)

# of ways 7 can be arranged in a circular pattern = 6! # of ways 2 can be seated together = 2.5!

# of ways 2 children cannot be seated together in a circular pattern = 6! - 2.5!.

Is this the OA ? Please explain how did you get 2.5!

Thanks

take for example a and b as the two children. they sit in the first and second position. next to them there are 5*4*3*1 possible ways to sit the other children. we multiply by 2 because there are even more ways when a and b switch their seats.

I'M completely lost here.

Let's say we have seats A-G. i.e. A,B,C,D,E,F,G then, the no. of ways 2 people can stay together is:

AB, BC, CD, DE, EF, FG, GA (7.2 = 14 ways!)

this is a problem of circular permutation. imagine a circle with 3 seats A B C:

first arrangement is A B C
second is A C B

that is because the circle can be rotated. that is why we use (n-1)! instead of n! for the total ways of arrangements.