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Questionหาค่า 3 หลักคู่ โดยใช้เลขซ้ำหรือไม่ซ้ำกันทั้งหมด (0-9)

Studdy Solution

STEP 1

Assumptions1. We are looking for three-digit numbers. . The numbers must be even.
3. We consider numbers with repeated and non-repeated digits.

STEP 2

First, let's find the three-digit even numbers with non-repeated digits.For a three-digit number to be even, the last digit must be an even number. The possible even digits are0,2,4,6, and8. However, since we are considering three-digit numbers, the first digit cannot be0. So, the first digit can be any digit from1 to9, the second digit can be any of the remaining9 digits, and the third digit can be any of the5 even digits excluding the ones already chosen.
Number of non−repeated even three−digit numbers=9times9times5Number\, of\, non-repeated\, even\, three-digit\, numbers =9 \\times9 \\times5

STEP 3

Calculate the number of non-repeated even three-digit numbers.
Number of non−repeated even three−digit numbers=9times9times5=405Number\, of\, non-repeated\, even\, three-digit\, numbers =9 \\times9 \\times5 =405

STEP 4

Next, let's find the three-digit even numbers with repeated digits.For a three-digit number to be even and have repeated digits, the first two digits can be any digit from1 to9, and the last digit must be the same as one of the first two digits. So, we have9 choices for the first digit,1 choice for the second digit (same as the first), and1 choice for the third digit (same as the first or second).
Number of repeated even three−digit numbers=9times1times1Number\, of\, repeated\, even\, three-digit\, numbers =9 \\times1 \\times1

STEP 5

Calculate the number of repeated even three-digit numbers.
Number of repeated even three−digit numbers=9times1times1=9Number\, of\, repeated\, even\, three-digit\, numbers =9 \\times1 \\times1 =9

STEP 6

Now, add the number of non-repeated and repeated even three-digit numbers to find the total number of three-digit even numbers.
Total number of three−digit even numbers=Number of non−repeated even three−digit numbers+Number of repeated even three−digit numbersTotal\, number\, of\, three-digit\, even\, numbers = Number\, of\, non-repeated\, even\, three-digit\, numbers + Number\, of\, repeated\, even\, three-digit\, numbers

STEP 7

Plug in the values for the number of non-repeated and repeated even three-digit numbers to calculate the total number of three-digit even numbers.
Total number of three−digit even numbers=405+9Total\, number\, of\, three-digit\, even\, numbers =405 +9

STEP 8

Calculate the total number of three-digit even numbers.
Total number of three−digit even numbers=405+=414Total\, number\, of\, three-digit\, even\, numbers =405 + =414There are414 possible three-digit even numbers that can be formed with repeated and non-repeated digits.

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