What is 47C4 + 51C3\(\mathop \sum \limits_{{\rm{j}} = 2}^5\) 52-jC3 equal to?

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NDA (Held On: 18 Sept 2016) Maths Previous Year paper
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  1. 52C4
  2. 51C5
  3. 53C4
  4. 52C5

Answer (Detailed Solution Below)

Option 1 : 52C4
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Detailed Solution

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Concept:

  • 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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