Probability Question (1 Viewer)

[coyney]

A group of 7 people sit around a table. In how many ways can
they be arranged if 2 people cannot sit together?

Cheers

 

[iBibah]

A group of 7 people sit around a table. In how many ways can
they be arranged if 2 people cannot sit next to each other?

Cheers

Cannot sit next to each other?

Also this is permutations not probability.

 

[coyney]

Cannot sit next to each other?

Also this is permutations not probability.

Oh yeah sorry, fixed.

 

[Aesytic]

you can find the number of arrangements where 2 cannot sit together by subtracting the number of arrangements where these 2 do sit together from the total number of arrangements with no restrictions
number of arrangements with no restrictions is 6!
number of arrangements where 2 people sit together would be 5!2!, by grouping the 2 specific people as one group
.'. number of arrangements where 2 don't sit together would be 6! - 5!2!

 

[ahdil33]

First order the two people.

Assume the first of the two people sits in one of the 7 seats.

1 x ....

The second person can now seat in 4 possible seats, not next to him, and not in the seat the first person already occupies, so.

1 x 4 ...

Now there's 5 people remaining, so there's 5! way they can be sorted.

The answer should be then, 1 x 4 x 5! = 480.

EDIT: Answer is the same as Aesytic's above. Do it whatever way you find more logical, or learn both if you can.

 

[coyney]

Aesytic has got it.