Question

A 9-digit phone number needs to be created. If no digit may be repeated, how many phone numbers are possible? [Hint: Phone number is allowed to start with a zero] \( 10 ! \) \( 2 \times 10 ! \) \( 9 ! \) \( 9 ! \times 10 ! \) \( 9 \times 9 ! \)

Answer 1

A total number of 9 digit numbers having different digit is given by :

\(^{10}P_9-^9P_8=\frac{10!}{1!}-\frac{9!}{1!}=10!-9!\)

= 10 × 9! - 9!

= 9! (10 - 1)

= 9! × 9