Question

Number of even numbers greater than \[300\] that can be formed with the digits \[1,2,3,4,5\] such that no digit being repeated is,
1. \[111\]
2. \[900\]
3. \[600\]
4. \[800\]

Answer 1

Hint: To solve this question we need to know which numbers are can be placed as the first digit with satisfying the given conditions, which numbers can be placed as the second digit with satisfying the given conditions, as same as for third, fourth, and fifth digits to find the total possibilities. Also, this question involves arithmetic operations.

Complete step-by-step answer:
In this questions, the given conditions are shown below,
The number should be an even number
The number would be greater than \[300\]
The numbers should be \[1,2,3,4,5\]
Repeated number not acceptable
We know that one-digit and two-digit numbers shouldn't be greater than \[300\] . So, we start at three-digit numbers.
According to the condition, \[3\] the first number should be \[3,4,5\]
According to the condition, \[1\] the last number should be \[2,4\]
 \[3 - \] Digit numbers,
If the first digit is \[3or5\] , the last digit can be \[2or4\] and the second digit can be any of the remaining digits. So, we have
 \[
   - - - \\
   \downarrow \downarrow \downarrow \\
  223 \\
 \]
 \[2 \times 2 \times 3 = 12\]
If we take the first digit is \[4\] , then the last digit is to be \[2\] and the remaining digits can be any of the three terms.
So, we get
 \[
   - - - \\
   \downarrow \downarrow \downarrow \\
  113 \\
 \]
 \[1 \times 1 \times 3 = 3\]
So, the possibilities for \[3 - \] digit term is,
 \[12 + 3 = 15\]
By using the same process for \[4 - \] digit term, we get
 \[
   - - - - \\
   \downarrow \downarrow \downarrow \downarrow \\
  4322 \\
 \]
 \[4 \times 3 \times 2 \times 2 = 48\]
By using the same process for \[5 - \] digit term, we get
 \[
   - - - - - \\
   \downarrow \downarrow \downarrow \downarrow \downarrow \\
  43212 \\
 \]
 \[4 \times 3 \times 2 \times 1 \times 2 = 48\]
So, we get
The total possibilities \[ = \] Number of possibilities in \[\left( {3digit + 4digit + 5digit} \right)\]
The total possibilities \[ = 15 + 48 + 48 = 111\]
So, the final answer is,
Total possibility \[ = 111\]
So, the option \[1)\] \[111\] is the correct answer.

So, the correct answer is “Option 1.”.

Note: This question involves the arithmetic operations like addition. Subtraction. Multiplication/ division. For these type of questions read the conditions carefully which was given in the question. Note that the final answer would be completely found according to the conditions given in the question.