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wvspidermonkey
07-16-2008, 08:56 AM
Ten nominees for three business awards are randomly seated at the 10 places at a round table. Three of these nominees are then called up together to receive the three awards. What is the probasbility that no two adjacent seats will be left empty?

1/3 2/5 5/12 7/16 1/2


Ok, I calculated that the total possible was (10 C 3)= 120, and I'm alright to the point that 10 X 6.

Answer explaination given... "10 ways in which three adjacent nominees could be called and 10 x 6 = 60."

I thought that 10 C 2 = 45 for the two consecutive locations and random third. Could you explain the why 10x6?

Thank you,

kevin
07-24-2008, 05:00 PM
You need to separate into cases to avoid double counting. Also the order of the choice does not matter!