00:01
In this problem, we are given the digits, and they are 0 ,1, 3, 4, 5, followed by 7 and 9, and we have to determine the number of different 5 -digit even numbers that we can form using the digits that we have above, provided that the repetition of digits in this 5 -digit even number that are not allowed.
00:26
So we will consider n as the number of different such 5 -digit even numbers that can make and that's what we have to get here.
00:34
So first we count and we see that there are in total seven number of digits that are given to us.
00:41
And out of these seven digits, the even digits are zero and four only.
00:47
So let's make five different boxes where each box represents a digit in a five digit even number.
00:53
So here we may have two possibilities.
00:56
The first possibility is that the last box is occupied by the digit.
01:01
So in this case, as the reputation is not allowed, we will be left with six other digits.
01:07
So we will have six ways to fill the first box, five ways to fill the second, four ways to fill the third, and only three ways to fill the fourth box.
01:16
And the other possibility could be that the last box is occupied by the digit zero, and four here because that is already occupied in this first case...