Math Questions. Only Geniouses. I need the answer?

Question

You have a deck of 26 cards, each labeled with one of the 26 letters of the alphabet.(Each letter appears on exactly one card.) Suppose you choose three cards at random, one at a time, from this deck. What is the probability that you choose your cards in alphabetical order? (Example: choosing G, then R, then X is in alpahbetical order, but choosing R, then G, then X is not.) Don't make an approximation and tell me how you got the answer

Answer 1

Ok, I got 1/6, which I think is quite reasonable.

So you are saying the 3 letters doesn't have to be consecutively alphabetical, right? For example, B, K, R is still considered alphabetical; it doesn't have to be BCD, right?

If so, then the answer should be 1/6:

This is how I got it:

Pick any random 3 letters in the alphabet, say M, G, D.
How many ways can you pick these 3 letters? - 6
MGD, MDG, GMD, GDM, DMG, DGM
And out of these 6 possible sequence, only one is in alphabetical order => DGM,

And this is true for any 3 random letters out of the 26 that you have.

So the chance of picking your cards in alphabetical order is:
1/6

Answer 2

unless the first card picked is Y or Z, you need to subtract that letter from 26, and it's that number over 25 on the chances of the second being in order. (Let's say you pick G first...there are only 19 after that which would be in order, so odds of second card in order are 19 divided by 25)If the first card picked is Y or Z, it is impossible to have 3 in a row alphabetically. The odds on the second card is how ever many letters remain in the alphabet behind the first letter, divided by 25 (number remaining after one pick) and if the first two are not in order, the third does not matter. If the first two are in order, the odds on the third are however many remain in the alphabet after that one, divided by 24 (that's how many are left after you picked two). Lets say the second card you picked is a W. Then the odds on the third card are 3 divided by 24--3 cards are eligible to be in order--you have 24 left)These events are only related if the first and second are in order, otherwise the possibility is ZERO.

Answer 3

The chance that you choose an A on the first try is one in 26, then the chance you choose B from the remaining cards is one in 25 and so on. So the chances of you choosing ABC etc is one in 26 times 25 times 24 times 23 and continue until you get to one.

Answer 4

My guess is 1 in 6. It doesn't matter the number of cards in the deck, just the number of options. If you picked abc, then your options are abc,acb,bac,bca, and cab, cba. I used to try to figure out how many options there were in my parents garage door opener when I was younger and still liked math. There were 5 numbers in the code. The numbers don't have to be in any order Alot more options there. What is your guess? Even better, my wep on my wireless in 9 numbers, chosen randomly, how many options? If I am wrong I blame it on the whiskey, but it makes sense at this point in time.

Answer 5

Yep Dusie did it right