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What is the value ofC(51, 21) - C(51, 22) + C(51, 23) - C(51, 24) + C(51, 25) - C(51, 26) + C(51, 27) - C(51, 28) + C(51, 29) - C(51, 30) ?
Concept: Formulae nCr ?= nCn-1?Calculation:Given,C(51, 21) - C(51, 22) + C(51, 23) - C(51, 24) + C(51, 25) - C(51, 26) + C(51, 27) - C(51, 28) + C(51, 29) - C(51, 30)We know that nCr ?= nCn-rSo we can write,C(51, 21) = C(51, 30)C(51, 22) = C(51, 29)C(51, 23) = C(51, 28)C(51, 24) = C(51, 27)C(51, 25) = C(51, 26)So the above expression can be written as C(51, 30) - C(51, 29) + C(51, 28) - C(51, 27) + C(51, 26) - C(51, 26) + C(51, 27) - C(51, 28) + C(51, 29) - C(51, 30)= C(51, 30) - C(51, 30) + C(51, 29) - C(51, 29) + C(51, 28) - C(51, 28) + C(51, 27) - C(51, 27) + C(51, 26) - C(51, 26)= 0Checking option C:C(51, 51) - C(51, 0)Using nCr ?= nCn-1 we can write C(51, 51) = C(51, 0),C(51, 0) - C(51, 0) = 0? The value of the expression is C(51, 51) - C(51, 0).
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