Question

How many 6-digit even number can be formed from the degi 1,2,3,4,5,6 and 7 so that the digits should not repeat and the second last digit is even?

Answer 1

Here the repetition is strictly not allowed. And it's given that the second last digit, i.e., the tens digit, must be even. Also the whole 6 digit number is an even number, so the ones digit must be an even digit.

First consider the ones digit place. This place can be occupied by 3 even numbers since there are only 3 ones. Once the ones place is filled, the tens place can be filled by 2 remaining even numbers.

Now two even numbers are taken, and we have 5 digits remaining. These 5 digits can be filled in the remaining 4 places in 5P4 = 5 × 4 × 3 × 2 = 120 ways.

Hence the required no. of 6 digit even numbers is 120 × 2 × 3 = 720.

#answerwithquality

#BAL