Probality question?

Question

Each of the eight letters in the word “IDITAROD” is written on a card. The cards are put into a bowl. The cards are drawn at random one at a time without replacement and placed from left to right in the order in which they are drawn. What is the probability the letters on the cards correctly spell “IDITAROD”? Express your answer as a common fraction.

Answer 1

The chance of pulling the first letter correctly is 2/8
The chance of pullling the second letter correctly is 2/7
The chance of pulling the third letter correctly is 1/6
The chance of pulling the fourth letter correctly is 1/5
The chance of pulling the fifth letter correctly is 1/4
The chance of pulling the sixth letter correcty is 1/3
The chance of pulling the seventh letter correctly is 1/2
The chance of pullling the last letter correctly is 1!

All of the chances given above are assuming that the correct letters have been pulled up to that point. The reason the probability of the first two terms has a two in the numerator is that those letters occur twice in the word. But when we get to those letters the second time, there will be only one instance of the letter left. The denominators keep going down, because there are fewer letters left to choose from.

So the chance of pulling them all correctly is:
(using * as the multiplication operator)

2/8 * 2/7 * 1/6 * 1/5 * 1/4 * 1/3 * 1/2 * 1

= 4/40320 = 1/1080

Answer 2

The probability of pulling them in an acceptable order is the number of ways to pull the letter divided by the total number of ways to pull the letters.

It turns out that there are four acceptable ways to pull them out: In their original order, or almost original order with the D's exchanged, almost original order with I's exchanged, orwith both I's and D's exchanged.

[Note: In general the number of way a word can be scrambled and reconstructed is the factoral of the counts of the letters multiplied together. So for iditarod,there are 2 i's, 2 d's and one each of t, a, r, and o. So the total is 2! * 2! * 1! *1! * 1! *1! = 4]

The total number of ways to pull the letters out are 8!

so the probability is 4/8!
= 4/ 40320
= 1/10080

Answer 3

[ 2/8 * 1/7 ] * [2/6 * 1/5] etc
[ I (2 ways to do ] [ D 2 wayus to do ] etc

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Important notice: Some or all of this answer was written by gjmb1960 visitor of yahoo answers Farm. For reliable information of any sort, you must consult an officially qualified professional in your local area. You use this at your own risk.