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Let a r = r 4 C r , b r = 4 - r 4 C r , A r = a r 2 3 b r and A = ∑ r = 0 4 A r , then the value of A is equal to

Correct answer

874

Step-by-step solution

A = ∑ r = 0 4 A r = ∑ r = 0 4 r   4 C r ∑ r = 0 4 2 ∑ r = 0 4 3 ∑ r = 0 4 4 - r   4 C r Now, ∑ r = 0 4 r   4 C r = ∑ r = 0 4 4 - r   4 C r = 4 × 2 3 = 2 5 A = 32 10 15 32 A = 1024 - 150 = 87 4

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