If the number of selections of r as well as (n + r) things from 5n different things are equal, then what is the value of r?
2n
We are given that the number of selections of r things and (n + r) things from 5n different things are equal. This can be written mathematically as:[ \binom{5n}{r} = \binom{5n}{n+r} \]. Using the symmetry property of binomial coefficients, which states that \( \binom{n}{k} = \binom{n}{n-k} \), we can equate the terms. This implies that \( r \) must be equal to \( 2n \). Therefore, the value of r is 2n.
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