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        riddles >> easy >> Combination with partial repetition
        
(Message started by: fatball on Nov 7^th, 2016, 1:21pm)

Title: Combination with partial repetition
Post by fatball on Nov 7^th, 2016, 1:21pm

Can anyone help please?

To start with, I am to pick 4 numbers out of 10 with repetition allowed; thus, there is a total of 10,000 possibilities. What is the outcome if 2 out of the 4 picks are the same in any order please?

Thanks!!

Title: Re: Combination with partial repetition
Post by dudiobugtron on Nov 7^th, 2016, 9:51pm

Sounds like a question that came straight out of a text book or homework assignment.

If that's true, though, then either it is poorly worded, or you have changed the wording. So we don't actually know what you want to work out. Are you wanting to know the probability that at least 2 out of the 4 picks will be the same?

Title: Re: Combination with partial repetition
Post by towr on Nov 7^th, 2016, 11:02pm

Two out of four the same, sound to me like three different numbers and one extra equal to one of those first three. So ten choices for the first, nine for the second, eight for the third and three for the fourth. But intuition and probability don't always mesh, so always double check :P

[e]Funnily enough, you should indeed double, so good thing I checked. There is, after all, two ways to order the repeated number (I could have started from the other end).
Another way, first pick the repeat number, so ten choice for the first, 1 choice for the second (repeat of the first number), then 9 choices for third, and 8 choices for the last. And a 3 factorial multiplier (=6) for covering different orders.[/e]

Title: Re: Combination with partial repetition
Post by fatball on Nov 8^th, 2016, 7:28am

Dudiobugtron, it is not a textbook question but one of my own. What I want to know is the distinct outcome based on my defined criteria.

Towr, thanks and since your answer of 720 includes a permutation of the two non-identical numbers, I would say the distinct outcome would be 360 if order is not important.