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$The digits 1, 2, 3, 4, and 5 are randomly arranged to form a three-digit number. (Digits are not repeated.) Find the probability that the number is even and greater than 500 . The probability that the three-digit number is even and greater than 500 is ◻. (Type an integer or a simplified fraction.)$

The digits $1$ , $2$ , $3$ , $4$ , and $5$ are randomly arranged to form a three-digit number. (Digits are not repeated.) Find the probability that the number is even and greater than $500$ . $\newline$ The probability that the three-digit number is even and greater than $500$ is $\square$ . $\newline$ (Type an integer or a simplified fraction.)

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Grade 8

Write a linear equation from a slope and a point

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Q. The digits

1

2

3

4

, and

5

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

500

\newline

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

500

\square

\newline

(Type an integer or a simplified fraction.)

Determine total possible numbers: Determine the total number of possible three-digit numbers. $\newline$ Since the digits are not repeated, the first digit can be chosen in $5$ ways, the second in $4$ ways, and the third in $3$ ways. $\newline$ Total number of possible three-digit numbers = $5 \times 4 \times 3 = 60$ .
Find ways for even numbers: Determine the number of ways to form an even three-digit number. An even number must end in $2$ or $4$ . Since the last digit can be chosen in $2$ ways, the first digit (hundreds place) can be chosen in $2$ ways ( $5$ or $4$ , to make the number greater than $500$ ), and the middle digit can be chosen in $3$ ways. Number of ways to form an even three-digit number greater than $500 = 2 \times 2 \times 3 = 12$ .
Calculate probability: Calculate the probability. $\newline$ The probability is the number of favorable outcomes divided by the total number of possible outcomes. $\newline$ Probability = Number of favorable outcomes / Total number of possible outcomes = $\frac{12}{60}$ .
Simplify fraction: Simplify the fraction. Simplify $\frac{12}{60}$ to its lowest terms. $\frac{12}{60} = \frac{1}{5}$ .