\({}^{m+n}C_r=\sum_{k=0}^{r}{}^{m}C_k{}^{n}C_{r-k}\) किस counting split से सिद्ध होता है?
The identity \({}^{m+n}C_r=\sum_{k=0}^{r}{}^{m}C_k{}^{n}C_{r-k}\) is proved by which counting split?
Explanation opens after your attempt
B. दो groups से कुल (r) चुनने में (k) पहले group से लेनाTaking (k) from the first group while selecting total (r) from two groups
Concept
In total (r) selections, the count from the first group varies as (k). In exams connect two-source selection with Vandermonde identity.
Why this answer is correct
The correct answer is B. दो groups से कुल (r) चुनने में (k) पहले group से लेना / Taking (k) from the first group while selecting total (r) from two groups. In total (r) selections, the count from the first group varies as (k). In exams connect two-source selection with Vandermonde identity.
Exam Tip
कुल (r) selection में first group का count (k) बदलता है। परीक्षा में two-source selection को Vandermonde identity से जोड़ें।
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