Dear Kona

You asked: "When should the order be considered and when it shouldn't be?"

I'll try to help you with this doubt.

Let's say there are 26 small tiles lying in a heap. Each tile has one letter of the English alphabet inscribed on it, and no two tiles have the same alphabet. Now you are asked by the tile-owners to pick up 2 tiles from this heap.

They are simply asking you to pick up the tiles; they are not interested in the order in which you pick up the tiles. Nothing will happen to one tile because it was picked up first, or because it was picked up second. So, whether you pick up E first and J later, or J first and E later doesn't matter. So, you will simply apply the formula to select a bunch of r things out of a bunch of n things =nCr.

When would order matter?

It would matter if they had told you that they will start the name of their new-born baby with the alphabet on the first tile you picked up. And that if the alphabet on your second slide lies between A and G, you will get $10. So, in this case, there are consequences to the order in which the tiles were picked up. You may still have picked up E and J, but the order in which you picked up will decide whether the baby will be named Eugene or Jeannie, and whether you will get $10 or not.

So, let's now tackle a question: What is the probability that the baby's name started with E and you got $10?

Total number of ways to pick up 1st tile = 26

Total number of ways to pick up 2nd tile = 25

So, Total number of ways to pick up the two tiles = 26*25

(Note that we didn't take 26C2, because 26C2 applies when you are taking out a bunch of 2 things out of a bunch of 26 things and order doesn't matter)

Favorable Cases:

Total number of ways in which the 1st tile can be E = 1

Total number of ways in which $10 can be won on the second tile = 6 (There are 7 alphabets from A to G, but E has already been taken out in the first pick)

So, Desired probability = (1*6)/(26*25)

=3/325

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Please press Kudos if you were helped by my post!