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JEE Advanced2018MathematicsBinomial TheoremActual

Let X = 10 C 1 2 + 2 10 C 2 2 + 3 10 C 3 2 + … + 10 10 C 10 2 , where 10 C r , r ∈ 1,2 , … . , 10 denote binomial coefficients. Then, the value of 1 1430 X is ______ .

Correct answer

0

Step-by-step solution

X = ∑ r = 0 n r . n C r 2 ; n = 10 X = n . ∑ r = 0 n n C r . n - 1 C r - 1 X = n . ∑ r = 1 n n C n - r . n - 1 C r - 1 X = n . 2 n - 1 C n - 1 ; n = 10 X = 10 . 19 C 9 X 1430 = 1 143 . 19 C 9 = 646

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