# Probability question, trying to find a solution!

The alphabet is written out onto paper and then cut up into 26 squares so that each letter is on one piece of paper. Four letters are drawn randomly without replacement. Work out the probability that these letters can be arranged to form WORD.

(seems like a pretty easy question to solve, right?)
Well, the answer is not 4/26 because that answer has been written down and it's been marked incorrect.
I've gone about it as when each letter is pulled out, the amount of chances there are decreases, eg. picking out an O is 1/26, then picking out an D is 1/25, then picking up an W is 1/24 and so on. I then tried multiplying them together, but that didn't work out.

I've thought of other ways to try and find a solution, but I'm struggling, and i would appreciate if any one could help me out to figure it out.
Thanks.

 Unknown008 Posts: 8,147, Reputation: 3745 Uber Member #2 Nov 9, 2011, 09:21 PM
Notice that the question says that the letters CAN be arranged to form WORD.

You can pick:
WORD in this order, or
DORW or,
ORDW etc.

Each of them will have a probability of $\frac{1}{26\times25\times24\times23}$

 emmaanne01 Posts: 2, Reputation: 10 Junior Member #3 Nov 11, 2011, 04:24 PM
That makes more sense, I was close.
Thank you!

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