How many even numbers lying between 200 & 500 can be formed from the digits 1,2,3,4,5,6, if no digits appears more than once in any number?
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The even numbers between 200 and 500 can be of the form like ABC.
The even numbers between 200 and 500 can be of the form like ABC.'A' can take values like 2, 3 and 4. Let us take an instance where A equals to 2. For that particular instance 'C' can have two values i.e 4 & 6. At the same time 'B' can occupy any of the remaining 4 digits. We can find such 2x4=8 combinations out there.
The even numbers between 200 and 500 can be of the form like ABC.'A' can take values like 2, 3 and 4. Let us take an instance where A equals to 2. For that particular instance 'C' can have two values i.e 4 & 6. At the same time 'B' can occupy any of the remaining 4 digits. We can find such 2x4=8 combinations out there. Now say if 'A' is equals to 3. 'C' can take any of the digits of 2,4 & 6. For each case 'B' has 4 distinct values. The number of occurrences in this case is 3x4=12.
The even numbers between 200 and 500 can be of the form like ABC.'A' can take values like 2, 3 and 4. Let us take an instance where A equals to 2. For that particular instance 'C' can have two values i.e 4 & 6. At the same time 'B' can occupy any of the remaining 4 digits. We can find such 2x4=8 combinations out there. Now say if 'A' is equals to 3. 'C' can take any of the digits of 2,4 & 6. For each case 'B' has 4 distinct values. The number of occurrences in this case is 3x4=12.The calculation is same as in the first case if 'A' equals to 4. The number of combinations are 8 in this case.
The even numbers between 200 and 500 can be of the form like ABC.'A' can take values like 2, 3 and 4. Let us take an instance where A equals to 2. For that particular instance 'C' can have two values i.e 4 & 6. At the same time 'B' can occupy any of the remaining 4 digits. We can find such 2x4=8 combinations out there. Now say if 'A' is equals to 3. 'C' can take any of the digits of 2,4 & 6. For each case 'B' has 4 distinct values. The number of occurrences in this case is 3x4=12.The calculation is same as in the first case if 'A' equals to 4. The number of combinations are 8 in this case.Therefore , the total number of even numbers found in this method is 8+12+8=28.
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