To solve this problem, we need to consider the different cases for the number of digits in the number.

1. One-digit numbers: The only even one-digit number is 2. So, there is 1 such number.

2. Two-digit numbers: The units place must be an even number. So, there are 2 choices (2 and 4) for the units place. The tens place can be any of the remaining 4 digits. So, there are 4 choices for the tens place. Therefore, there are 2*4 = 8 such numbers.

3. Three-digit numbers: Again, the units place must be an even number. So, there are 2 choices for the units place. The hundreds place can be any of the remaining 4 digits, so there are 4 choices for the hundreds place. The tens place can be any of the remaining 3 digits, so there are 3 choices for the tens place. Therefore, there are 2*4*3 = 24 such numbers.

4. Four-digit numbers: The units place must be an even number. So, there are 2 choices for the units place. The thousands place can be any of the remaining 4 digits, so there are 4 choices for the thousands place. The hundreds place can be any of the remaining 3 digits, so there are 3 choices for the hundreds place. The tens place can be any of the remaining 2 digits, so there are 2 choices for the tens place. Therefore, there are 2*4*3*2 = 48 such numbers.

5. Five-digit numbers: The units place must be an even number. So, there are 2 choices for the units place. The ten thousands place can be any of the remaining 4 digits, so there are 4 choices for the ten thousands place. The thousands place can be any of the remaining 3 digits, so there are 3 choices for the thousands place. The hundreds place can be any of the remaining 2 digits, so there are 2 choices for the hundreds place. The tens place can be the remaining 1 digit, so there is 1 choice for the tens place. Therefore, there are 2*4*3*2*1 = 48 such numbers.

Adding up all these cases, there are 1 + 8 + 24 + 48 + 48 = 129 even numbers less than 500 that can be formed using the digits 1, 2, 3, 4, and 5 each only once.

Question

To solve this problem, we need to consider the different cases for the number of digits in the number.

1. One-digit numbers: The only even one-digit number is 2. So, there is 1 such number.

2. Two-digit numbers: The units place must be an even number. So, there are 2 choices (2 and 4) for the units place. The tens place can be any of the remaining 4 digits. So, there are 4 choices for the tens place. Therefore, there are 2*4 = 8 such numbers.

3. Three-digit numbers: Again, the units place must be an even number. So, there are 2 choices for the units place. The hundreds place can be any of the remaining 4 digits, so there are 4 choices for the hundreds place. The tens place can be any of the remaining 3 digits, so there are 3 choices for the tens place. Therefore, there are 2*4*3 = 24 such numbers.

4. Four-digit numbers: The units place must be an even number. So, there are 2 choices for the units place. The thousands place can be any of the remaining 4 digits, so there are 4 choices for the thousands place. The hundreds place can be any of the remaining 3 digits, so there are 3 choices for the hundreds place. The tens place can be any of the remaining 2 digits, so there are 2 choices for the tens place. Therefore, there are 2*4*3*2 = 48 such numbers.

5. Five-digit numbers: The units place must be an even number. So, there are 2 choices for the units place. The ten thousands place can be any of the remaining 4 digits, so there are 4 choices for the ten thousands place. The thousands place can be any of the remaining 3 digits, so there are 3 choices for the thousands place. The hundreds place can be any of the remaining 2 digits, so there are 2 choices for the hundreds place. The tens place can be the remaining 1 digit, so there is 1 choice for the tens place. Therefore, there are 2*4*3*2*1 = 48 such numbers.

Adding up all these cases, there are 1 + 8 + 24 + 48 + 48 = 129 even numbers less than 500 that can be formed using the digits 1, 2, 3, 4, and 5 each only once.

Knowee AI · Accepted Answer

To solve this problem, we need to consider the different cases for the number of digits in the number.

1. One-digit numbers: The only even one-digit number is 2. So, there is 1 such number.

2. Two-digit numbers: The units place must be an even number. So, there are 2 choices (2 and 4) for the units place. The tens place can be any of the remaining 4 digits. So, there are 4 choices for the tens place. Therefore, there are 2*4 = 8 such numbers.

3. Three-digit numbers: Again, the units place must be an even number. So, there are 2 choices for the units place. The hundreds place can be any of the remaining 4 digits, so there are 4 choices for the hundreds place. The tens place can be any of the remaining 3 digits, so there are 3 choices for the tens place. Therefore, there are 2*4*3 = 24 such numbers.

4. Four-digit numbers: The units place must be an even number. So, there are 2 choices for the units place. The thousands place can be any of the remaining 4 digits, so there are 4 choices for the thousands place. The hundreds place can be any of the remaining 3 digits, so there are 3 choices for the hundreds place. The tens place can be any of the remaining 2 digits, so there are 2 choices for the tens place. Therefore, there are 2*4*3*2 = 48 such numbers.

5. Five-digit numbers: The units place must be an even number. So, there are 2 choices for the units place. The ten thousands place can be any of the remaining 4 digits, so there are 4 choices for the ten thousands place. The thousands place can be any of the remaining 3 digits, so there are 3 choices for the thousands place. The hundreds place can be any of the remaining 2 digits, so there are 2 choices for the hundreds place. The tens place can be the remaining 1 digit, so there is 1 choice for the tens place. Therefore, there are 2*4*3*2*1 = 48 such numbers.

Adding up all these cases, there are 1 + 8 + 24 + 48 + 48 = 129 even numbers less than 500 that can be formed using the digits 1, 2, 3, 4, and 5 each only once.

How many even numbers less than 500 can be formed using the digits 1, 2, 3, 4 and 5? Each digit may beused only once in any number.

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