Question

According to the given conditions, how many 7-digit numbers are possible with the form ABC-XXXX, where X and A can be digits 1-7, B can be digits 0-8, and C can be digits 1-8?

a) 1,210,104
b) 9,235,216
c) 2,164,384
d) 6,235,014
e) None of the above

Answer 1

To find the number of possible 7-digit numbers of the form ABC-XXXX with given conditions for A, B, C, and X, we multiply the number of possibilities for each digit. The calculation yields 1,209,216, which does not match any of the provided options; therefore, the answer is 'None of the above'.

Step-by-step explanation:

The question asks how many 7-digit numbers with the form ABC-XXXX are possible given specific conditions for each digit. We can calculate this by looking at the number of possibilities for each digit and then multiplying them together:

• For digit A, we have 7 possibilities since it can be any digit from 1 to 7.
• For digit B, there are 9 possibilities (0-8).
• For digit C, we have 8 possibilities because it can be any digit from 1 to 8.
• For each 'X', we have 7 possibilities since they can also be digits from 1 to 7.

Now we multiply the possibilities for each slot: 7 (A) * 9 (B) * 8 (C) * 74 (XXXX).

Calculating this gives us 7 * 9 * 8 * 2401, which equals 1,209,216.

The closest answer to this result from the choices provided is a) 1,210,104, but since our calculation does not match exactly, the correct answer is e) None of the above.