The question in the image asks:

"How many different seven-digit telephone numbers can be formed if the first digit cannot be zero?"

Solution:

A telephone number is made up of 7 digits. If the first digit cannot be zero, we have the following constraints:

1. The first digit can be any number between 1 and 9, so there are 9 possible choices (1-9).
2. The remaining six digits can be any number between 0 and 9, so each of these six positions has 10 possible choices.

To find the total number of possible telephone numbers, we multiply the number of choices for each digit:

$\text{Total numbers} = 9 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10$

This simplifies to:

$9 \times 10^6 = 9,000,000$

Thus, there are 9,000,000 different seven-digit telephone numbers that can be formed if the first digit cannot be zero.

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. How many 7-digit numbers can be formed if the first two digits cannot be zero?
2. If the first digit must be even, how many different seven-digit numbers can be formed?
3. What is the probability of randomly generating a 7-digit number starting with 5?
4. How many distinct 6-digit numbers can be formed if repetition of digits is not allowed?
5. If the second digit also cannot be zero, how does that change the total number of 7-digit numbers?

Tip: When solving counting problems, always check if there are any restrictions on the digits or positions to avoid miscalculations.