Letters of the word CASABLANCA are written on identical cards and shuffle.Four cards are then picked one after the other without replacement. Determine the probability that the four letter picked are C, A,N, A in that order

Question

Letters of the word CASABLANCA are written on identical cards and shuffle.Four cards are then picked one after the other without replacement. Determine the probability that the four letters picked are C, A,N, A in that order 

Answer 1

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.