# Thread: probability of choosing number

1. ## probability of choosing number

I have a question related to probability of choosing numbers.

If there is 5 people picking numbers from 1 to 5, there is 5^5 ways to pick numbers.

The question is, what is the probability of 2 people choosing same number, and 3 people choosing distinct number?

For example, {1, 1, 2, 3, 4} or {1,4,5,2,4}

My attempt:

Since there is 2 same number and 3 distinct number, I assumed picking 3 number from 5, and 2 number from 5, and multiplied them and divided it by 5^5.

But not sure if I did this correctly.

Thank you!

2. ## Re: probability of choosing number

There are 1,200 sequences out of 3,125 that satisfy your requirement of two similar numbers and three distinct ones being drawn. To see this, first figure the number of ways that persons 1 and 2 can draw the same number and persons 3, 4 and 5 each draw a number that is different from those already drawn. Then think about in how many ways each of those sequences can be arranged.

Your description of what you have tried suggests that you got the right answer but for the wrong reason.

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