Fido10
Bunuelwe are looking for the probability that the 5 numbers picked ( picked one by one) are in ascending order,
If we know that n=5, we can have at the 1st pick x1, at the 2nd pick x2 at the 3rd pick x3, at the 4th pick x5 we'll then have a selection of (x1,x2,x3,x4,x5) this is a case of ascending order
If actually we pick at first x1, at 2nd x2 at 3rd x3 at 4th x4 but at 5th x6, then we would have picked a selection ( x1,x2,x3,x4,x6) which is a selection also in ascending order, So we have more than one case of a selection in ascending order !!!
Can you explain
Take a simple case. I have a list of numbers, say 3, 6, 7, 10, 11, 20.
I select two numbers out of these. What is the probability that I selected the smaller one first?
When I select 2 numbers, there are only 2 ways of selecting them: Smaller first and greater later & greater first and smaller later.
So the probability that I select smaller first is 1/2.
Does it have anything to do with exactly which numbers I select? No. I select two numbers - that is given to me. They could be any two numbers, I don't care.
I only want the find the probability of picking the smaller one before the greater one.
Same is our case here. When we select 5 numbers, no matter which 5 numbers, we can do it in 5! different sequences. Say we selected 3, 6, 7, 10, 11.
We could have selected them in 5! different ways - 3, 6, 7, 10, 11 or 6, 11, 10, 3, 7 or 10, 3, 6, 7, 11 etc.
There is only one way in which the list is in ascending order and that is 3, 6, 7, 10, 11.
So our probability is 1/5!
If selection was our concern too, then we would need statement 1 too because that would tell us how many total selections are possible. But it is not concern. Only the arrangement of the selected numbers (the order in which we pick them) is our concern.
Answer (B)
dave13