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.

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- Nov 1st 2006, 04:17 AMpunmasterProbability
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 PMearboth
- Nov 1st 2006, 12:42 PMThePerfectHacker
Here is another way.

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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,

$\displaystyle 18\cdot 6=108$

The possible outcomes is the number of ways of selecting 3 out of twenty.

Which is,

$\displaystyle _{20}C_3=1140 $

Thus,

$\displaystyle \frac{108}{1140}$ - Nov 1st 2006, 01:04 PMPlato
There are 18 subsets of three consecutive integers.

There are $\displaystyle _{20}C_3=1140 $ total subsets three integers.

Thus, $\displaystyle \frac{18}{1140} = 0.01579$

The order does not come to this.

If we do use order then we would have $\displaystyle \frac{108}{(20)(19)(18)} = 0.01579$ - Nov 1st 2006, 01:07 PMThePerfectHacker