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 that a phone number is a sequence of 10 digits, where each digit can range from 0 to 9.

Identify the constraints: the 1st and 4th digits cannot be 0. This means for these positions, the digits can range from 1 to 9.

Calculate the number of possibilities for the 1st digit. Since it cannot be 0, there are 9 possible choices (1 through 9).

Calculate the number of possibilities for the 4th digit. Similarly, since it cannot be 0, there are 9 possible choices (1 through 9).

Calculate the number of possibilities for the remaining 8 digits (2nd, 3rd, 5th, 6th, 7th, 8th, 9th, and 10th). Each of these can be any digit from 0 to 9, giving 10 possible choices for each. Multiply the possibilities for each digit position to find the total number of possible phone numbers.

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a. Compute the probability that 10 people have 10 different birthdays. Hint: The first person's birthday can occur 365 ways, the second person's birthday can occur 364 ways, because he or she cannot have the same birthday as the first person, the third person's birthday can occur 363 ways, because he or she cannot have the same birthday as the first or second person, and so on.

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Textbook Question

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b. The FBI does not allow the first character to be 0. To the nearest billion, how many identification numbers are possible?

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Multiple Choice

How many possible outcomes are there if you roll 5 dice?

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Jumble Many newspapers carry “Jumble,” a puzzle in which the reader must unscramble letters to form words. The letters MHRHTY were included in newspapers on the day this exercise was written. How many ways can those letters be arranged? Identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.

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Expected Value in North Carolina’s Pick 4 Game In North Carolina’s Pick 4 lottery game, you can pay \$1 to select a four-digit number from 0000 through 9999. If you select the same sequence of four digits that are drawn, you win and collect \$5000.

a. How many different selections are possible?

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Struggling with Statistics?

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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Fundamental Counting Principle practice set

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?