00:01
In this problem, we are asked to find out the number of four digit numbers which are less than 4 ,599 and they are formed using the digits 1 ,2, 3, 4, 5, 6 and 7.
00:27
So we can divide this into two cases.
00:33
The first case is when the number is less than 4 ,000 and the second case is when the number lies between 4 ,000 and 4 ,598.
00:55
So here, let us first look at the first case.
00:59
So in case 1 we look at the numbers that are less than 4 ,000.
01:04
So here since we are looking at a 4 digit number we have four spaces that need to be filled.
01:10
The first space can be filled by the numbers 1, 2 and 3 since these are the numbers which are less than fro.
01:20
So we have three options for filling the first space.
01:23
For the second space there is no restriction.
01:26
So we have a total of seven options.
01:31
So we have seven.
01:32
Likewise for the third space and for the fourth one.
01:35
So we have three times seven times seven times seven numbers, which are less than 4 ,000 and that can be formed with a given seven digits.
01:48
Next, let us look at the second case.
01:50
So this consists of the numbers that lie between 4 ,000 and 4 ,598...