Question

Geraldine is picking a four-digit password by using the digits 0 through 9. She can use each digit only once. How many different passwords are possible?

34.

40.

5,040.

10,000

Answer 1

`\displaystyle 5040`

Step-by-step Step-by-step explanation:

You have ten digits, but can only choose from four each time. Therefore, you will use the formula pertaining to permutations [order matters]. Here is how it is done:

`\displaystyle (n!)/([-k + n]!) = {}_nP_k \\ \\ (10!)/([-4 + 10]!) = (10!)/(6!) \Longrightarrow ([2][3][4][5][6][7][8][9][10])/([2][3][4][5][6]) \\ \\ \\ \boxed{5040} = [7][8][9][10]`

So, there will be five thousand forty different passwords, or in this case, combinations.

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