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#885436 - 05/03/13 11:28 PM Li'l probber...
CanukDenis Offline
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Registered: 11/26/00
Posts: 14923
Loc: Ottawa Ontario Canada
6 balls: 2 weigh 1 unit each, 2 weigh 2 units each and 2 weigh 3 units each.

The 6 balls are placed at random on a balance scale: 3 on each side.

What is the probability that the the scale will balance?
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#885623 - 05/04/13 08:13 PM Re: Li'l probber... [Re: CanukDenis]
BobH Online   content
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Registered: 10/14/11
Posts: 1393
Loc: 47.79N, 122.24W
1 in 15 is what I get.

a) 720 permutations total (6!)
b) it will only balance with a 1 2 3 on each side
c) call the balls 1a 1b 2a 2b 3a 3b then there are 6 permutations of any set of 3 balls on one side (3!)
d) there are 8 combinations of a balls or b balls taken in a group of 1 2 and 3.
e) 6*8=48
f) 48 in 720 = 1 in 15

now I hope I didn't make a mistake and my assumptions were correct. smile
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I've learned that if you're too busy to help a friend, you're too busy.

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#885654 - 05/04/13 11:28 PM Re: Li'l probber... [Re: CanukDenis]
CanukDenis Offline
Adept Boomer

Registered: 11/26/00
Posts: 14923
Loc: Ottawa Ontario Canada
Sorry Bob, but too low.

Hint: probability is more than 1/3
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#885666 - 05/05/13 03:36 AM Re: Li'l probber... [Re: CanukDenis]
CCbomber Offline
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Registered: 01/16/03
Posts: 2915
Loc: Mojave desert, California
2/5

(6 C 3) = 20

As bob said, there are 8 combinations with 1,2,3
on each side of the scale.

8/20 = 2/5

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#885683 - 05/05/13 06:53 AM Re: Li'l probber... [Re: CanukDenis]
BobH Online   content
Addicted Boomer

Registered: 10/14/11
Posts: 1393
Loc: 47.79N, 122.24W
aha, I didn't account for the fact that you are really just picking 3 of the 6 to be on one side.

That is surprisingly high.
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Bob
I've learned that if you're too busy to help a friend, you're too busy.

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#885717 - 05/05/13 11:49 AM Re: Li'l probber... [Re: CanukDenis]
CanukDenis Offline
Adept Boomer

Registered: 11/26/00
Posts: 14923
Loc: Ottawa Ontario Canada
2/5 correct.

Easier still:
since 1,2,3 is a must, then:
1: 1 or 2 or 3: probability = 1
2: (assume 1 was 1st) 2 or 3: prob. = 4/5
3: (assume 2 was 2nd) 3 : prob. = 1/2

1 * 4/5 * 1/2 = 2/5
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