Question

There are four students, all of different heights, who are to be randomly arranged in a line. What is the probability that the tallest student will be first in line and the shortest student will be last in line?

Answer 1

`1/12`

Explanation:

Assuming you have a set front and end of the line (ie only one end of the line can be classed as first)

The probability that the tallest student is 1st in line `= 1/4`

Now, the probability that the shortest student is 4th in line `= 1/3` (If the tallest person is first in line he can't also be last)

The total probability `= 1/4 * 1/3 = 1/12`

If there is no set front and end of the line (ie either end can be first) then it's just the probability that short as at one end and tall at other then you get

`1/12` (the probability that the short one is at one end and the tall one at the other) `+ 1/12` (the probability that the tall one is at one end and the short one at the other) `= 2/12 = 1/6`