Question

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.). How many seven digit phone numbers are possible with
these restrictions?






A. 5,120,000

B. 5,114,80

C. 4,608,000

D. 10,000,000

Answer 1

B. 5,114,800

Explanation:

Digit A can be 0 through 7. That is 8 choices.

8

Digits B and C can be any digit from 1 to 8. That is 8 choices.

8 × 8 × 8

Digits D, E, F, and G can be any digit from 1 to 9. That is 10 choices.

8 × 8 × 8 × 10 × 10 × 10 × 10 = 5,120,000

Digits D, E, F, and G cannot all be the same digit.

8 × 8 × 8 = 512

There are 512 numbers ending in 0000, 512 numbers ending in 1111, etc.

512 × 10 = 5,120

There are 5,120 numbers which end in 4 equal digits. We subtrac that number from our total.

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