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1. Toni needs to create a 4-digit password for her cell phone using only the numbers 0 through 9 for each digit. Each number can only be used once. How many permutations of possible passwords could she create?



Answer :

GinnyAnswer

Final answer:

The answer explains how to calculate permutations for a 4-digit password with no repetition using the formula for permutations.


Explanation:

Permutations of 4-digit password:

  1. To calculate the permutations for a 4-digit password with no repetition, use the formula for permutation: [tex]$^nP_r = rac{n!}{(n - r)!}$[/tex]
  2. For this case, with 10 options for the first digit, 9 for the second, 8 for the third, and 7 for the fourth, the total number of permutations is: [tex]$^{10}P_4 = rac{10!}{(10 - 4)!} = 5040$[/tex]
  3. Therefore, Toni could create 5040 permutations of possible 4-digit passwords using the numbers 0 through 9 with each number used only once.

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