Question

(b) As in part (a), how many three-digit phone prefixes are possible that do not start with 0 or 1, but contain 0 or 1 as the middle digit

Answer 1

Answer:

The number of 3-digit phone prefixes that do not start with 0 or 1, but contain 0 or 1 as the middle digit is 160.

Step-by-step explanation:

The phone prefix for any area is of the form X X X.

These prefixes can take values from 0 to 9.

The condition to create a phone prefix is:

• The first digit cannot be 0 or 1
• The middle digit is either 0 or 1.

The possible number of ways to fill the first place is 8 since 0 or 1 cannot be the first digit.

The possible number of ways to fill the second place is 2 since the middle digit can be occupied by either 0 or 1.

The possible number of ways to fill the last place is 10 since there are no condition applied to the last digit.

Then the number of phone prefixes that can be formed is = $8\times2\times10=160$

Thus, the possible number of phone prefixes possible is 160.