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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 given digits without repetition.
Calculate Favorable Outcomes: There are $6$ choices for the first digit, $5$ choices for the second digit, and $4$ choices for the third digit, since the digits cannot be repeated. This gives us a total of $6 \times 5 \times 4 = 120$ possible three-digit numbers.
Find Probability: Now we need to find the number of favorable outcomes, which are the even numbers greater than $600$ . Since the number must be even, the last digit must be $2$ , $4$ , or $6$ .
Find Probability: Now we need to find the number of favorable outcomes, which are the even numbers greater than $600$ . Since the number must be even, the last digit must be $2$ , $4$ , or $6$ .For a number to be greater than $600$ , the first digit must be either $6$ . There is only $1$ choice for the first digit.
Find Probability: Now we need to find the number of favorable outcomes, which are the even numbers greater than $600$ . Since the number must be even, the last digit must be $2$ , $4$ , or $6$ .For a number to be greater than $600$ , the first digit must be either $6$ . There is only $1$ choice for the first digit.Since the first digit is $6$ and the last digit must be even, we have $3$ choices for the last digit ( $2$ , $4$ , or $6$ ). However, since $6$ is already used as the first digit, we only have $2$ choices left for the last digit ( $2$ or $4$ ).
Find Probability: Now we need to find the number of favorable outcomes, which are the even numbers greater than $600$ . Since the number must be even, the last digit must be $2$ , $4$ , or $6$ .For a number to be greater than $600$ , the first digit must be either $6$ . There is only $1$ choice for the first digit.Since the first digit is $6$ and the last digit must be even, we have $3$ choices for the last digit ( $2$ , $4$ , or $6$ ). However, since $6$ is already used as the first digit, we only have $2$ choices left for the last digit ( $2$ or $4$ ).For the middle digit, we have $4$ remaining digits to choose from ( $1$ , $3$ , $2$ $9$ , or the unused even number). This gives us $4$ choices for the middle digit.
Find Probability: Now we need to find the number of favorable outcomes, which are the even numbers greater than $600$ . Since the number must be even, the last digit must be $2$ , $4$ , or $6$ .For a number to be greater than $600$ , the first digit must be either $6$ . There is only $1$ choice for the first digit.Since the first digit is $6$ and the last digit must be even, we have $3$ choices for the last digit ( $2$ , $4$ , or $6$ ). However, since $6$ is already used as the first digit, we only have $2$ choices left for the last digit ( $2$ or $4$ ).For the middle digit, we have $4$ remaining digits to choose from ( $1$ , $3$ , $2$ $9$ , or the unused even number). This gives us $4$ choices for the middle digit.Multiplying the number of choices for each position, we get $1$ (for the first digit) * $4$ (for the middle digit) * $2$ (for the last digit) = $4$ $4$ favorable outcomes.
Find Probability: Now we need to find the number of favorable outcomes, which are the even numbers greater than $600$ . Since the number must be even, the last digit must be $2$ , $4$ , or $6$ .For a number to be greater than $600$ , the first digit must be either $6$ . There is only $1$ choice for the first digit.Since the first digit is $6$ and the last digit must be even, we have $3$ choices for the last digit ( $2$ , $4$ , or $6$ ). However, since $6$ is already used as the first digit, we only have $2$ choices left for the last digit ( $2$ or $4$ ).For the middle digit, we have $4$ remaining digits to choose from ( $1$ , $3$ , $2$ $9$ , or the unused even number). This gives us $4$ choices for the middle digit.Multiplying the number of choices for each position, we get $1$ (for the first digit) * $4$ (for the middle digit) * $2$ (for the last digit) = $4$ $4$ favorable outcomes.The probability is the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability is $4$ $5$ .
Find Probability: Now we need to find the number of favorable outcomes, which are the even numbers greater than $600$ . Since the number must be even, the last digit must be $2$ , $4$ , or $6$ .For a number to be greater than $600$ , the first digit must be either $6$ . There is only $1$ choice for the first digit.Since the first digit is $6$ and the last digit must be even, we have $3$ choices for the last digit ( $2$ , $4$ , or $6$ ). However, since $6$ is already used as the first digit, we only have $2$ choices left for the last digit ( $2$ or $4$ ).For the middle digit, we have $4$ remaining digits to choose from ( $1$ , $3$ , $2$ $9$ , or the unused even number). This gives us $4$ choices for the middle digit.Multiplying the number of choices for each position, we get $1$ (for the first digit) $4$ $2$ $4$ (for the middle digit) $4$ $2$ $2$ (for the last digit) $4$ $6$ $4$ $7$ favorable outcomes.The probability is the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability is $4$ $8$ .We can simplify the fraction $4$ $8$ by dividing both the numerator and the denominator by $4$ $7$ . This gives us $6$ $1$ .