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Question

The value of 50C4+r=1656-rC3 is


A

56C4

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B

56C3

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C

55C33

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D

55C4

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Solution

The correct option is A

56C4


Explanation for correct option:
Given expression is 50C4+r=1656-rC3
50C4+r=1656-rC3=50C4+55C3+54C3+53C3+52C3+51C3+50C3
=50C4+50C3+55C3+54C3+53C3+52C3+51C3=51C4+51C3+55C3+54C3+53C3+52C3[nCr+nCr-1=n+1Cr]=52C4+52C3+55C3+54C3+53C3=53C4+53C3+55C3+54C3=54C4+54C3+55C3=55C4+55C3=56C4

Hence, option(A) is correct


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