Question

A seven digit telephone number is of the form ABC-DEFG. In one particular state, the

Answer 1

Answer:

Choice B. 5,114,880 (There's a digit missing in the problem.)

Step-by-step explanation:

You must see the number of choices you have for each digit. Then you multiply all those numbers of choices together.

There are 7 digits in the phone number, so you will be multiplying 7 numbers together.

_ * _ * _ * _ * _ * _ * _

First digit: any digit except 8 and 9.

Since you exclude 2 digits from the 10 possible digits, there are 8 choices left.

8 * _ * _ * _ * _ * _ * _

Second and third digits: any digit from 1 and 8.

Any digit from 1 to 8 means: 1, 2, 3, 4, 5, 6, 7, 8. That means there are 8 choices.

8 * 8 * 8 * _ * _ * _ * _

Last four digits: no restrictions (for now), so there are 10 choices for each digit. We will deal with the restriction of 4 equal digits below.

8 * 8 * 8 * 10 * 10 * 10 * 10

The product of the 7 numbers above is:

8 * 8 * 8 * 10 * 10 * 10 * 10 = 5,120,000

The last 4 digits cannot all be thee same. There are 10 ways they can all be the same: 0000, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999.

Each of the combinations of the first 3 digits cannot have 10 combinations of equal digits.

The number of combinations of the first 3 digits is: 8 * 8 * 8 = 512.

Each of these 512 combinations cannot have 10 combinations of equal digits for the last 4 digits. 512 * 10 = 5120.

We must subtract 5120 from 5,120,000 to find the final answer.

5,120,000 - 5120 = 5,114,880

Answer 2

Answer:

B. 5,114,80

Step-by-step explanation:

A seven digit telephone number is of the form ABC-DEFG. In one particular state, the  digit ‘A’ can be any digit except 8 and 9. The digits B and C can be any digit from 1 - 8.  The digits D, E, F, and G can be any digit 0 – 9 except they can’t all be the same (e.g. 0000, 1111, 2222, ….etc.). Therefore, 5,114,80 seven digit phone numbers are possible with  these restrictions.