Question
Download Solution PDFWhat is 47C4 + 51C3 + \(\mathop \sum \limits_{{\rm{j}} = 2}^5\) 52-jC3 equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- nCr + nCr+1 = n+1Cr+1
Calculation:
We have to find the value of 47C4 + 51C3 + \(\mathop \sum \limits_{{\rm{j}} = 2}^5\) 52-jC3
47C4 + 51C3 + \(\mathop \sum \limits_{{\rm{j}} = 2}^5\) 52-jC3
= 47C4 + 51C3 + 50C3 + 49C3 + 48C3 + 47C3
= (47C3 + 47C4) + 51C3 + 50C3 + 49C3 + 48C3
= (48C3 + 48C4) + 51C3 + 50C3 + 49C3
= (49C3 + 49C4) + 51C3 + 50C3
= (50C3 + 50C4) + 51C3
= 51C3 + 51C4
= 52C4
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