If 4 numbers from 1 to 100 are chosen at random, one at a time, find the probability that they will be chosen in decreasing order.

jamesbroadman Feb 27, 2020

#3

#5**0 **

It does not at all matter whether there are 100 numbers or just 4. The best way to approach the problem is to consider drawing just two numbers. So you've drawn two distinct numbers: what is the probability that the first one will be less than the second? Well, there are just two ways to draw two chosen numbers: the smallest either come first or last, meaning that the probability of drawing two numbers in their natural order is 1/2.

When it comes to four numbers, there are 24 permutations of four objects and thus 24 ways to draw a given set of four numbers. Only in one permutation, out of 24, will all four numbers be in descending order.

Guest Feb 28, 2020