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A nice combinatorics proof!

There are \(n\) numbers,\(x_1,x_2,x_3,...x_{n-1},x_n\),\(r\) numbers out of these \(n\) are chosen,each number,\(x_i;i\in [1,n]\) occurs in how many of these sets of numbers?\[\] I have posted mine below.\[\] Post yours too!

Note by Adarsh Kumar
1 year, 1 month ago

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Let us check how many times,\(x_i\) can come in a set of \(r\) numbers,it will come whenever the rest of the \(r-1\) numbers can be chosen differently.And the number of ways the \(r-1\) numbers can be chosen out of the \(n-1\) numbers,excluding\(x_i\)is,\((n-1)_{\huge{C}_{\huge{r-1}}}\).And done! Adarsh Kumar · 1 year, 1 month ago

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