यदि \(^{n}C_{r-2}:{}^{n}C_{r-1}:{}^{n}C_r\) दिए हों, तो formula derivation में कौन-सा ratio सबसे पहले उपयोगी होगा?
If \(^{n}C_{r-2}:{}^{n}C_{r-1}:{}^{n}C_r\) is given, which ratio is most useful first in the derivation?
Explanation opens after your attempt
Correct Answer
A. \(\frac{{}^{n}C_{r-1}}{{}^{n}C_{r-2}}=\frac{n-r+2}{r-1}\)
Concept
Factorial cancellation in consecutive combinations gives this ratio. In exams use adjacent ratios instead of calculating long values.
Why this answer is correct
The correct answer is A. \(\frac{{}^{n}C_{r-1}}{{}^{n}C_{r-2}}=\frac{n-r+2}{r-1}\). Factorial cancellation in consecutive combinations gives this ratio. In exams use adjacent ratios instead of calculating long values.
Exam Tip
Consecutive combinations में factorial cancellation से यह ratio मिलता है। परीक्षा में लंबी values निकालने के बजाय adjacent ratio लगाएं।
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