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Hint: It's not as difficult as it seems. It's the number of ways the friends can form a circle divided by the number of ways the names can be drawn out of the hat.
1/10

For a group of n friends, there are n! (n factorial) ways to draw the names out of the hat. Since a circle does not have a beginning and end, choose one person as the beginning and end of the circle. There are now (n-1)! ways to distribute the remaining people around the circle. Thus the probability of forming a single circle is

(n-1)! / n!

Since n! = (n-1)! * n (for n > 1), this can be rewritten as

(n-1)! / (n*(n-1)!)

Factoring out the (n-1)! from the numerator and denominator leaves

1/n

as the probability.
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Waking In Woods Riddle

Hint:
Half way. After that you are walking out of the woods.
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Barking In The Backseat Riddle

Hint:
Put him in the front seat of the car
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A Kind Of Fish That Can Never Swim Riddle

Hint:
A dead fish
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Cracked Made Told And Played Riddle

Hint:
A Joke
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Made Of Sugar And Soda Riddle

Hint:
Snake (Firework)
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Mummies Tell No Secrets Riddle

Hint:
Because they keep things under wraps.
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A Train Leaves From Halifax Riddle

Hint:
Both trains would be at the same spot when they meet therefore they are both equally close to Halifax.
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Hangs On The Wall And Falls Riddle

Hint:
A Barometer
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Piece Of Burned Wood Riddle

Hint:
Chard!
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I Can Fall Off A Building And Live Riddle

Hint:
Paper
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Made By Light Riddle

Hint:
A shadow
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Eats Shoots And Leaves Riddle

Hint:
Pandas

"Eats-shoots-leaves." Pandas "eat", then "shoot" then "leave".
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If A Red House Is Made From Red Bricks Riddle

Hint:
Greenhouses are always made of glass.
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What Kind Of Apple Is Not An Apple Riddle

Hint:
A pineapple
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