00:00In this question, we are asked, the number of strictly increasing functions from this set to this set.
00:06And, f of i, function of i should not be equal to i.
00:09So, first of all, we can write this set as, it is 1, 2, 3, 4, 5, 6.
00:16Now, we have 9 outcomes.
00:18What? 1, 2, 3, 4, 5, 6, 7, 8, 9.
00:23For 1, it can be 1, function of 1 can be equal to 1.
00:26But, if function of 1 is equal to 1, then it will not satisfy this condition.
00:32So, function of 1 cannot be equal to 1.
00:35And, function of 2 cannot be equal to 1.
00:37Because, if function of 2 is equal to 1,
00:41Then, function of 1 will be, what?
00:44We will have no value for function of 1.
00:46Because, here we are given, it is a strictly increasing function.
00:51So, function of 2 can also be not equal to 1.
00:54So, any function cannot have the value 1.
00:56So, from this set, we will exclude 1 for now.
01:00If we exclude 1, how many numbers are we left with?
01:04We are left with 8 numbers now.
01:07And, we have to arrange them in serial ease.
01:11In this serial, only we have to arrange them.
01:13So, there is no serial wise arrangement.
01:16So, what will be the type of arrangement?
01:18In this, we will have to exclude 2 numbers,
01:21which we are not picking.
01:23Then, for example, we have excluded 3 and 4.
01:26Then, 2, for 1 outcome will be 2.
01:302 outcome will be 5, 3, 6, 4, 7, 5, 8, 6, 9.
01:35In the same way, we can exclude 2 and 5.
01:38Then, outcome for 1 will be 3, 2 will be 4.
01:42So, for each unique type of 2 number, we exclude.
01:45The outcome will be different.
01:47So, how many total number of unique types
01:49can we pick up any 2 numbers from this, these numbers?
01:54So, we know the formula of picking 2 numbers
01:57from a selected number of numbers is,
02:00the number of numbers,
02:02and below 6,
02:04the number we are picking,
02:05amount of numbers we are picking.
02:07So, there are 8 numbers,
02:09and we are picking 2 numbers.
02:10So, it becomes 8, 3, 2.
02:12It becomes 8 into 7, divided by 2.
02:16So, 2 for,
02:172 cancel 8 by 4.
02:19So, 7 into 4, 28.
02:21So, final answer will be 28.
