Answer:
Step-by-step explanation:
We have 10 digits:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
For the first place we have 10 digits to choose from.
For the second place we have 9 digits to choose from (one has already been chosen)
For the third 8 digits, and for the last 7.
Total 4-digit personal identification numbers is equal:
10 · 9 · 8 · 7 = 560
You can use the variations without repetition:
[tex]V^k_n=\dfrac{n!}{(n-k)!}[/tex]
Variation is a way of selecting k items from a collection of n items (k ≤ n), such that the order of selection does matter. The repetition of items is not allowed.
We have
n = 10, k = 4
Substitute:
[tex]V^{4}_{10}=\dfrac{10!}{(10-4)!}=\dfrac{6!\cdot7\cdot8\cdot9\cdot10}{6!}=7\cdot8\cdot9\cdot10=560[/tex]
The answer on Edge is B, or 5040.
If numbers range from 0-9 that means you start with 10 possible digits.
So: 10 x 9 x 8 x 7 = 5040.
