A website requires a four-digit numerical password in which the digits cannot repeat. How many possible passwords are there?
• 24
• 5,040
• 151,200
• 3,628,800
10 * 9 * 8 * 7 = ?
To find the number of possible passwords, we can break down the problem into four steps:
Step 1: Choose the first digit
Since the first digit cannot repeat, we have 10 choices (0-9).
Step 2: Choose the second digit
Since the second digit cannot repeat, we have 9 choices left (excluding the digit already chosen in Step 1).
Step 3: Choose the third digit
Since the third digit cannot repeat, we have 8 choices left (excluding the digits chosen in Steps 1 and 2).
Step 4: Choose the fourth digit
Since the fourth digit cannot repeat, we have 7 choices left (excluding the digits chosen in Steps 1, 2, and 3).
To find the total number of possible passwords, we multiply the number of choices for each step:
Total number of passwords = 10 choices for Step 1 * 9 choices for Step 2 * 8 choices for Step 3 * 7 choices for Step 4
Multiplying these numbers together gives us:
10 * 9 * 8 * 7 = 5,040
Therefore, the correct answer is 5,040.