Question

1. how many permutations of a 7-digit phone number exist if any number 0-9 may be used but repetition is not allowed?

\\(\frac{10!}{3!}\\)
70
\\(10^7\\)
10!

Explanation:

Step1: Recall Permutation Formula

The permutation formula for choosing \( r \) elements from \( n \) elements without repetition is \( P(n,r)=\frac{n!}{(n - r)!} \). Here, \( n = 10 \) (digits 0 - 9) and \( r = 7 \) (7 - digit phone number).

Step2: Substitute Values into Formula

Substitute \( n = 10 \) and \( r = 7 \) into the formula: \( P(10,7)=\frac{10!}{(10 - 7)!}=\frac{10!}{3!} \).

Answer:

\(\frac{10!}{3!}\) (the first option)