Manny needs to create a four-digit password for his cellphone. If no digits can be repeated, in how many ways can this task be done?a.5,040b.10,000c.210d.7,180
Question
Manny needs to create a four-digit password for his cellphone. If no digits can be repeated, in how many ways can this task be done?
a. 5,040
b. 10,000
c. 210
d. 7,180
Solution
To solve this problem, we need to use the concept of permutations.
Step 1: Manny has 10 choices (0-9) for the first digit of his password.
Step 2: For the second digit, since no digit can be repeated, he only has 9 choices left.
Step 3: For the third digit, he has 8 choices left.
Step 4: For the fourth and final digit, he has 7 choices left.
So, the total number of ways Manny can create his password is found by multiplying these choices together: 1098*7 = 5,040.
So, the answer is a. 5,040.
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