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?
- A. n
- B. 2n ✓
- C. 3n
- D. 4n
Correct Answer: B. 2n
Explanation
Given \binom{5n}{r} = \binom{5n}{n+r}. By the property \binom{N}{a} = \binom{N}{b} \implies a = b or a+b = N. Since r \neq n+r, we must have r + (n+r) = 5n, leading to 2r = 4n \implies r = 2n.
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