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Sagot :
The number of distinct values that we can draw(with replacement) is;
= [tex]\frac{ ((2n-1)!)}{ n!(n -1)! }[/tex]
Here,
The given set is = {1, 2, 3, ……, n}
n number of drawn from this set with replacement.
Then we have to find number of distinct values that we can draw.
What is combination?
The field of mathematics concerned with problems of selection, arrangement, and operation within a finite or discrete system.
Now,
The given set is = {1, 2, 3, ……, n}
n number of drawn from this set with replacement.
Since, we know we draw p things from q with replacement then
Number of ways = [tex]^{p+q-1} C_q[/tex]
Here number of element in the set = n
And number of element we have to draw with replacement = n
Therefore, number of distinct values that we can draw
= [tex]^{n+n-1} C_n[/tex]
= [tex]^{2n-1} C_n[/tex]
= [tex]\frac{(2n-1)!}{n!(2n -1 - n)!}[/tex]
= [tex]\frac{((2n-1)!)}{n!(n -1)!}[/tex]
Hence, The number of distinct values that we can draw(with replacement) is;
= [tex]\frac{ ((2n-1)!)}{ n!(n -1)! }[/tex]
To learn more about combination visit:
https://brainly.com/question/11732255
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