Class 11 Mathematics Permutations and Combinations Derivations of formulas and their connections Hard Level 65

यदि \(^{n}C_{r-1}:{}^{n}C_r=3:5\), तो ratio derivation में कौन-सा expression उपयोगी है?

If \(^{n}C_{r-1}:{}^{n}C_r=3:5\), which expression is useful in the ratio derivation?

Explanation opens after your attempt
Correct Answer

B. \(\frac{{}^{n}C_{r-1}}{{}^{n}C_r}=\frac{r}{n-r+1}\)

Step 1

Concept

Canceling factorials in consecutive combinations gives \(\frac{r}{n-r+1}\). In exams do not calculate full values in ratio questions.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{{}^{n}C_{r-1}}{{}^{n}C_r}=\frac{r}{n-r+1}\). Canceling factorials in consecutive combinations gives \(\frac{r}{n-r+1}\). In exams do not calculate full values in ratio questions.

Step 3

Exam Tip

Consecutive combinations में factorial cancel करने पर \(\frac{r}{n-r+1}\) मिलता है। परीक्षा में ratio questions में full values न निकालें।

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यदि \(^{n}C_{r-1}:{}^{n}C_r=3:5\), तो ratio derivation में कौन-सा expression उपयोगी है? / If \(^{n}C_{r-1}:{}^{n}C_r=3:5\), which expression is useful in the ratio derivation?

Correct Answer: B. \(\frac{{}^{n}C_{r-1}}{{}^{n}C_r}=\frac{r}{n-r+1}\). Explanation: Consecutive combinations में factorial cancel करने पर \(\frac{r}{n-r+1}\) मिलता है। परीक्षा में ratio questions में full values न निकालें। / Canceling factorials in consecutive combinations gives \(\frac{r}{n-r+1}\). In exams do not calculate full values in ratio questions.

Which concept should I revise for this Mathematics MCQ?

Canceling factorials in consecutive combinations gives \(\frac{r}{n-r+1}\). In exams do not calculate full values in ratio questions.

What exam hint can help solve this Mathematics question?

Consecutive combinations में factorial cancel करने पर \(\frac{r}{n-r+1}\) मिलता है। परीक्षा में ratio questions में full values न निकालें।