A secret code must consist of three capital letters followed by a digit. Letters cannot be repeated. How many secret codes are possible?
A.
140,400
B.
156,000
C.
175,760
D.
358,800
Assuming the code uses English alphabet,
Choices for first letter: 26
Choices for second letter: 26
Choices for third letter: 26
Choices for digit: 10
Total number of codes = product of all 4 choices.
To find the number of possible secret codes, we need to consider the number of choices for each position in the code.
Since the code consists of three capital letters followed by a digit, we can break down the calculation into two parts: the number of choices for the letters and the number of choices for the digit.
Number of choices for the letters:
For the first letter, there are 26 choices (A to Z). Once a letter is chosen, there are 25 choices remaining for the second letter, as we cannot repeat letters. Similarly, for the third letter, there are 24 choices left.
So, the total number of choices for the three letters is 26 * 25 * 24 = 15,600.
Number of choices for the digit:
Since the digit can be any of the ten possible digits (0 to 9), there are 10 choices.
To get the total number of possible secret codes, we multiply the number of choices for the letters by the number of choices for the digit:
15,600 * 10 = 156,000.
Therefore, the correct answer is B. 156,000.