To solve this problem, we need to understand the rule of divisibility by 9. A number is divisible by 9 if the sum of its digits is divisible by 9.

Step 1: Find the sum of the given digits: 0 + 1 + 2 + 3 + 4 + 7 + 8 = 25.

Step 2: Since 25 is not divisible by 9, we need to remove some digits to make the sum divisible by 9. The only way to do this is to remove 7 and 8, which gives us a sum of 10.

Step 3: Now we have 5 digits left (0, 1, 2, 3, 4) and we need to form a 5-digit number. However, since the number cannot start with 0 (as it would then be a 4-digit number), we have 4 choices for the first digit.

Step 4: For the remaining 4 places, we can use any of the 5 digits, including 0. So, we have 5 choices for the second place, 4 for the third, 3 for the fourth, and 2 for the fifth.

Step 5: Multiply these choices together to get the total number of 5-digit numbers that can be formed: 4 * 5 * 4 * 3 * 2 = 480.

However, this includes numbers that are not divisible by 9. To find the numbers that are divisible by 9, we need to divide this by the number of 5-digit numbers that can be formed with the digits 0, 1, 2, 3, 4, which is 5 * 5 * 4 * 3 * 2 = 600.

So, the total number of 5-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 7, 8 (without repetition) and are divisible by 9 is 480/600 = 0.8, which is not a whole number. Therefore, none of the given choices (216, 214, 212, 218) are correct.

Question

To solve this problem, we need to understand the rule of divisibility by 9. A number is divisible by 9 if the sum of its digits is divisible by 9.

Step 1: Find the sum of the given digits: 0 + 1 + 2 + 3 + 4 + 7 + 8 = 25.

Step 2: Since 25 is not divisible by 9, we need to remove some digits to make the sum divisible by 9. The only way to do this is to remove 7 and 8, which gives us a sum of 10.

Step 3: Now we have 5 digits left (0, 1, 2, 3, 4) and we need to form a 5-digit number. However, since the number cannot start with 0 (as it would then be a 4-digit number), we have 4 choices for the first digit.

Step 4: For the remaining 4 places, we can use any of the 5 digits, including 0. So, we have 5 choices for the second place, 4 for the third, 3 for the fourth, and 2 for the fifth.

Step 5: Multiply these choices together to get the total number of 5-digit numbers that can be formed: 4 * 5 * 4 * 3 * 2 = 480.

However, this includes numbers that are not divisible by 9. To find the numbers that are divisible by 9, we need to divide this by the number of 5-digit numbers that can be formed with the digits 0, 1, 2, 3, 4, which is 5 * 5 * 4 * 3 * 2 = 600.

So, the total number of 5-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 7, 8 (without repetition) and are divisible by 9 is 480/600 = 0.8, which is not a whole number. Therefore, none of the given choices (216, 214, 212, 218) are correct.

Knowee AI · Accepted Answer