a. If any seven digits could be used to form a telephone number, how many seven-digit telephone numbers would not have any repeated digits’?
b. How many seven-digit telephone numbers would have at least one repeated digit?
c. What is the probability that a randomly chosen seven-digit telephone number would have at least one repeated digit’?

(a)

To find seven-digit telephone numbers would not have any repeated digits if any seven digits could be used to form a telephone number.

Given information:

Calculate the number of 7 digit telephone numbers without any repeated digits.

Concept used:

The possibilities for the number of 7 digit telephone numbers without any repeated digits can be calculated as P(n,r).

Calculation:

Calculate the number of 7 -digit telephone numbers without any repeated digits. The total telephone number is 10 -digits

(b)

To find how many seven-digit telephone numbers would have at least one repeated digits.

(c)

To calculate the probability that the number of 7 -digit telephone numbers with at least one repeated digit.