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Question

The number of value(s) of r satisfying the equation 69C3r1 69Cr2= 69Cr21 69C3r is

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Solution

Given
69C3r1 69Cr2= 69Cr21 69C3r 69C3r1+ 69C3r= 69Cr2+ 69Cr21 70C3r= 70Cr23r=r2 or 3r+r2=70r=0,3 or r2+3r70=0r=0,3 or (r+10)(r7)=0r=0,3,10,7

As 3r1,r2,r21,3rW and less than or equal to 69, so the required values are
r=3,7

Hence, the number of values of r is 2.

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