The probability of picking a 'C' as the first letter is 1/10, as there is one 'C' and a total of 10 letters.

The probability of picking an 'A' as the second letter is 3/9 because there are three 'A's left, and you have already picked one letter.

The probability of picking an 'N' as the third letter is 1/8. There is only one 'N' left, and you have already picked two letters.

The probability of picking the last 'A' as the fourth letter is 2/7 because there are two 'A's left, and you have already picked three letters.

Now, multiply these probabilities together to find the overall probability:

(1/10) * (3/9) * (1/8) * (2/7) = 6/50400 = 1/8400

So, the probability that you will pick the letters C, A, N, and A in that order from the word CASABLANCA is 1/8400.