SOLUTION: If 4 numbers from 1 to 1000 are chosen at random, one at a time, find the probability that they will be chosen in decreasing order. My work: does 1/24 include the numbers like 9

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Question 1134955: If 4 numbers from 1 to 1000 are chosen at random, one at a time, find the probability that they will be chosen in decreasing order.
My work: does 1/24 include the numbers like 9998,7776,2221?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!

you got it right:
does include the numbers like 9998,7776,2221? no, you are given numbers from to

When numbers are chosen, there are possible permutations of them, influencing to their order.
Of this permutations, only one provides the requested decreasing order.
Therefore, the probability under the problem's question is .

Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website!
.

I solved this problem at least TWO TIMES before, and the number    came to you from my earlier posts.

See, for example, my response at the link

https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1134624.html

https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1134624.html

My answers were absolutely clear.

What is interesting, the answer remains the same for any other domain instead of the segment [1,1000].

For example, the answer remains the same for the domain [0,10000]; or for the domain [-10,100001];

or for domain (0,infinity)   (= all real positive numbers); and even for the domain (-infinity,infinity)   (= all real numbers).

If it is what you want to ask, then here you have my answer.