A security code consists of either five or six different letters. How many distinct security codes are possible
ANS:173659200
To find the number of distinct security codes possible, we need to consider two cases: one with five letters and one with six letters.
Case 1: Five letters
Since the code consists of different letters, we have a total of 26 options for the first letter, 25 options for the second letter (as it cannot be the same as the first), 24 options for the third letter, 23 options for the fourth letter, and 22 options for the fifth letter. Therefore, the number of distinct codes with five letters is:
26 * 25 * 24 * 23 * 22 = 789,360
Case 2: Six letters
Following the same logic, with six different letters, the first letter has 26 options, the second letter has 25 options, and so on until the sixth letter, which has 21 options. Hence, the number of distinct codes with six letters is:
26 * 25 * 24 * 23 * 22 * 21 = 64,090,560
Finally, to find the total number of distinct security codes, we sum the number of distinct codes in each case:
789,360 + 64,090,560 = 64,879,920