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Answer :
Final answer:
The number of passwords possible for a password consisting of 3 digits and 2 letters can be calculated using permutations. The total number of passwords is 397,440.
Explanation:
The number of possible passwords can be calculated by considering the number of choices for each digit or letter position. Since we need 3 digits and 2 letters, the number of choices for the digit positions is 10P3 (permutations of 10 elements taken 3 at a time) and the number of choices for the letter positions is 24P2 (permutations of 24 elements taken 2 at a time). To calculate the total number of passwords, we can multiply these two values together:
Total number of passwords = 10P3 * 24P2
Now, we can calculate the values:
10P3 = 10! / (10-3)! = 10! / 7! = 10 * 9 * 8 = 720
24P2 = 24! / (24-2)! = 24! / 22! = 24 * 23 = 552
Therefore, the total number of passwords is:
Total number of passwords = 720 * 552 = 397,440
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