Probability

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Nov 1st 2006, 04:17 AM
punmaster

Probability

A bag contains the numbers 1 through 20 inclusive. If three are selected at random and placed in order from smallest to largest, find the probability that the arrangement is of three consecutive integers.
Nov 1st 2006, 12:25 PM
earboth

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Quote:

Originally Posted by punmaster

A bag contains the numbers 1 through 20 inclusive. If three are selected at random and placed in order from smallest to largest, find the probability that the arrangement is of three consecutive integers.

Hello,

I made a diagram to analyze the described situation. Maybe you can use it for your calculations

EB
Nov 1st 2006, 12:42 PM
ThePerfectHacker

Quote:

Originally Posted by punmaster

A bag contains the numbers 1 through 20 inclusive. If three are selected at random and placed in order from smallest to largest, find the probability that the arrangement is of three consecutive integers.

Here is another way.
---
Probability is favorable to possible.

What is favorable?
{1,2,3} All premutations of this set = 6
{2,3,4} All premutations of this set = 6
.....
{18,19,20} All premutations of this set = 6
In total we have,
18 Sets
Thus,
$18\cdot 6=108$
The possible outcomes is the number of ways of selecting 3 out of twenty.
Which is,
$_{20}C_3=1140$

Thus,
$\frac{108}{1140}$
Nov 1st 2006, 01:04 PM
Plato

Quote:

Originally Posted by ThePerfectHacker

18 Sets Thus,
$18\cdot 6=108$
The possible outcomes is the number of ways of selecting 3 out of twenty.
Which is,
$_{20}C_3=1140$
Thus,
$\frac{108}{1140}$

There are 18 subsets of three consecutive integers.
There are $_{20}C_3=1140$ total subsets three integers.
Thus, $\frac{18}{1140} = 0.01579$

The order does not come to this.
If we do use order then we would have $\frac{108}{(20)(19)(18)} = 0.01579$
Nov 1st 2006, 01:07 PM
ThePerfectHacker

Quote:

Originally Posted by Plato

The order does not come to this.

You are right. When I was doing this problem I first did it with order then realized that order is not important. So I re-edited the problem but forgot to remove the 3!