I am not very good at probabitliuy. Can someone explain to me in detail how they get the 4 exclusion?
Can someone explain in detail how the answer is arrived?
Models: (Shortest) 1,2,3,4,5,6,7 (Tallest)
First collect all possible combinations of 5 models from 7 models.
7C5 = 21. (Any 5 selected can be made to stand in order of height)
Now it is required that 4th & 6th tallest model should not be together.
So, find out combnation of 5 models in which "5" is not there, because only when "5" is not there, 4 & 6 will be together, got it?
Let's see, how many combinations of 5 models are there (in 7C5) such that 4 & 6 is present but 5 is not present.
Consider 4 & 6 selected (i.e. 2 models are selected & remaining 3 are to be selected), so we are left with 1,2,3,5,7. We don't want "5", so we are now left with 1,2,3,7.
Now, in how many ways can we select remaining 3 models from these 4 models? 4C3 = 4.
Hence, total = 7C5 -4 = 21-4 = 17