Question

How many 6 digit even numbers can be formed from digits 1 to 7 so that the digits should not repeat and the second last digit is even?

Answer 1

Since, we have to form 6 digit even numbers can be formed from digits 1 to 7.

To form even numbers, units digit should be either 2,4 or 6. Therefore, there are three ways.

Now, since the second last digit is also even. Since, from the three numbers , one of the number is used in units place. Therefore, there are 2 ways for the second last digit, as the digits should not repeat.

Now, 5 numbers are left. There are 5! ways to fill the remaining digits.

Therefore, Total numbers formed = $5! \times 3 \times 2$

= 720 ways.

Therefore, 720, six digit even numbers can be formed.

Answer 2

Step-by-step explanation:

Since, we have to form 6 digit even numbers can be formed from digits 1 to 7.

To form even numbers, units digit should be either 2,4 or 6. Therefore, there are three ways.

Now, since the second last digit is also even. Since, from the three numbers , one of the number is used in units place. Therefore, there are 2 ways for the second last digit, as the digits should not repeat.

Now, 5 numbers are left. There are 5! ways to fill the remaining digits.

Therefore, Total numbers formed = 5! \times 3 \times 25!×3×2

= 720 ways.

Therefore, 720, six digit even numbers can be formed.