4. Probability

Fundamental Counting Principle

4. Probability

Fundamental Counting Principle

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Multiple Choice

Phone numbers are 10 digits long. How many possible phone numbers are there if the 1^st and 4^th numbers can't be 0?

$10$

$90$

$8,100,000,000$

$10,000,000,000$

Verified step by step guidance

Understand the problem: We need to calculate the total number of possible 10-digit phone numbers, given that the 1st and 4th digits cannot be 0.

Identify the constraints: The 1st and 4th digits can be any digit from 1 to 9, while the other digits (2nd, 3rd, 5th, 6th, 7th, 8th, 9th, and 10th) can be any digit from 0 to 9.

Calculate the number of choices for each digit: The 1st digit has 9 choices (1-9), the 4th digit has 9 choices (1-9), and each of the remaining 8 digits has 10 choices (0-9).

Use the multiplication principle: Multiply the number of choices for each digit to find the total number of possible phone numbers. The formula is: $9 \times 10 \times 10 \times 9 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10$.

Interpret the result: The product of these numbers will give the total number of possible phone numbers under the given constraints.

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Phone numbers are 10 digits long. How many possible phone numbers are there if the 1st and 4th numbers can't be 0?

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Phone numbers are 10 digits long. How many possible phone numbers are there if the 1^st and 4^th numbers can't be 0?