0:00
Hello everyone.
00:01
So in this question we have given permutations p1, p2, p3 and so on up to p9 of 1, 2, 2, till 9 such that p1 is greater than p2, greater than p3, greater than p4, less than p5, less than p6, less than p7, less than p8 and less than p9.
00:19
Now we have to find the number of all the permutations.
00:22
So now here we can see that p4 is less than p1, less than p2, less than p2, less than p2, less.
00:30
Than p3 we will name this to be equation 1 and p 4 is less than p 5 p 6 then less than p 7 less than p 8 less than p 9 and we will name this to be equation 2 so now from 1 and 2 from 1 and 2 we can say that p 4 is less than p 1 less than p 2 less than p 2 less than p 3 less than p5 less than p6 less than p7 less than p8 less than p9.
01:08
So which implies we can say that p4 is less than pi where i is equal to 1, 2, 3, 5, 6, 7, 8 and 9.
01:22
And here we have given set a whose elements are 1, 2, 3, 4, 5, 6, 6, 7, 8, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7.
01:31
7, 8 and 9.
01:34
And now we can see here that p4 is less than all the pis, which means p4 is the minimum element.
01:43
And here in the set a, the minimum element is 1.
01:47
So therefore we can say that p4 is equal to 1.
01:52
So now from 1, equation 1, so from equation 1, it is given that p1 is greater than p2 is greater than p3 is greater than p4 so which implies we can say that p1 is greater than p2 greater than p3 greater than 1 now we have to choose three from set a but p4 is 1 which means the number of elements number of elements left will be equal to 9 minus 1 which is equal to 8.
02:34
So there are 8 elements out of which we have to choose 3 element...