Problem Solving

In many ways can Ann, Bea, Cam, Don, Ella, and Fay be seated if Ann and Bea cannot be seated next to each other?

a) 240
b) 360
c) 480
d) 600
e) 720

Carloblacksun wrote:In many ways can Ann, Bea, Cam, Don, Ella, and Fay be seated if Ann and Bea cannot be seated next to each other?

a) 240
b) 360
c) 480
d) 600
e) 720

Bonjour Paris,

What you want to do is:

1) Find the possible seatings - without any restriction

A B C D E F = 6!

2) Have A & B sit next to each other and GLUE them together so they act like a Siamese twin

AB C D E F = 5!

and remember they can also switch places - :!:

BA C D E F = 5 !

3) Not If you subtract what you have just found from the all possible ways:

6! - 2 x 5 ! = 5! ( 6 - 2 ) = 120 x 4 = 480

same as logitech:
total ways = 6!
ways when Ann & bea always together = 5! *2 (consider Ann bea as one object and they themselves can be seated in 2 ways, therefore 5! multiplied by 2)
difference = when ann & bea never together = 5!(6-2)=480

thanks a lot guys! I am quite quick in calculation so it took 4/5 minutes to make the ABCDEF count, but this formula is much quicker...

would you consider this question EXTREMELY difficult or not so much?

Carloblacksun wrote:thanks a lot guys! I am quite quick in calculation so it took 4/5 minutes to make the ABCDEF count, but this formula is much quicker...

would you consider this question EXTREMELY difficult or not so much?

I hate to say this but it is very basic question for its types. This shit can get really ugly.