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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!

2 years, 2 months 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!

- 2 years, 2 months ago