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$The digits 1,2,3,4,5, and 6 are randomly arranged to form a three-digit number. (Digits are not repeated) Find the probability that the number is even and greater than 600 The probability that the three-digit number is even and greater than 600 is ◻ (Type an integer or a simplified fraction )$

The digits $1$ , $2$ , $3$ , $4$ , $5$ , and $6$ are randomly arranged to form a three-digit number. (Digits are not repeated) Find the probability that the number is even and greater than $600$ $\newline$ The probability that the three-digit number is even and greater than $600$ is $\square$ $\newline$ (Type an integer or a simplified fraction )

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Algebra 2

Even and odd functions

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Q. The digits

1

2

3

4

5

, and

6

are randomly arranged to form a three-digit number. (Digits are not repeated) Find the probability that the number is even and greater than

600

\newline

The probability that the three-digit number is even and greater than

600

\square

\newline

(Type an integer or a simplified fraction )

Determine total possible numbers: To find the probability that the number is even and greater than $600$ , we first need to determine the total number of possible three-digit numbers that can be formed with the digits $1,2,3,4,5$ , and $6$ without repetition.
Calculate total possible numbers: There are $6$ choices for the first digit, $5$ choices for the second digit, and $4$ choices for the third digit, since we are not allowing repetition of digits. Therefore, the total number of possible three-digit numbers is $6 \times 5 \times 4$ .
Find number of favorable outcomes: Calculating the total number of possible three-digit numbers: $6 \times 5 \times 4 = 120$ .
Calculate number of favorable outcomes: Now, we need to find the number of favorable outcomes, which are the even numbers greater than $600$ . For a number to be even, it must end in an even digit ( $2$ , $4$ , or $6$ ).
Calculate probability: Since the number must be greater than $600$ , the first digit must be $6$ . There is only $1$ choice for the first digit.
Calculate probability: Since the number must be greater than $600$ , the first digit must be $6$ . There is only $1$ choice for the first digit.For the last digit, which determines if the number is even, we have $2$ choices ( $2$ or $4$ , since $6$ is already used as the first digit).
Calculate probability: Since the number must be greater than $600$ , the first digit must be $6$ . There is only $1$ choice for the first digit.For the last digit, which determines if the number is even, we have $2$ choices ( $2$ or $4$ , since $6$ is already used as the first digit).For the middle digit, we have $4$ remaining choices ( $1$ , $3$ , $6$ $0$ , or the remaining even number that was not used for the last digit).
Calculate probability: Since the number must be greater than $600$ , the first digit must be $6$ . There is only $1$ choice for the first digit.For the last digit, which determines if the number is even, we have $2$ choices ( $2$ or $4$ , since $6$ is already used as the first digit).For the middle digit, we have $4$ remaining choices ( $1$ , $3$ , $6$ $0$ , or the remaining even number that was not used for the last digit).Calculating the number of favorable outcomes: $1$ (for the first digit) $6$ $2$ $4$ (for the middle digit) $6$ $2$ $2$ (for the last digit) $6$ $6$ .
Calculate probability: Since the number must be greater than $600$ , the first digit must be $6$ . There is only $1$ choice for the first digit.For the last digit, which determines if the number is even, we have $2$ choices ( $2$ or $4$ , since $6$ is already used as the first digit).For the middle digit, we have $4$ remaining choices ( $1$ , $3$ , $6$ $0$ , or the remaining even number that was not used for the last digit).Calculating the number of favorable outcomes: $1$ (for the first digit) $6$ $2$ $4$ (for the middle digit) $6$ $2$ $2$ (for the last digit) $6$ $6$ .The probability is the number of favorable outcomes divided by the total number of possible outcomes. So, the probability that the number is even and greater than $600$ is $6$ $8$ .
Calculate probability: Since the number must be greater than $600$ , the first digit must be $6$ . There is only $1$ choice for the first digit.For the last digit, which determines if the number is even, we have $2$ choices ( $2$ or $4$ , since $6$ is already used as the first digit).For the middle digit, we have $4$ remaining choices ( $1$ , $3$ , $6$ $0$ , or the remaining even number that was not used for the last digit).Calculating the number of favorable outcomes: $1$ (for the first digit) $6$ $2$ $4$ (for the middle digit) $6$ $2$ $2$ (for the last digit) $6$ $6$ .The probability is the number of favorable outcomes divided by the total number of possible outcomes. So, the probability that the number is even and greater than $600$ is $6$ $8$ .Simplifying the fraction $6$ $8$ gives us $1$ $0$ .