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Class 11MathematicsPermutations and CombinationsCombinationsExpert
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What is the value of (\sum_{r=0}^{4}{}^{7}C_{r},{}^{5}C_{4-r})?

Answer and explanation

Correct answer: 495

Using Vandermonde’s identity, \(\sum_{r=0}^{4}{}^{7}C_r\,{}^{5}C_{4-r}={} ^{7+5}C_4={} ^{12}C_4\). Therefore, the value is \(495\). Option 330 equals \({}^{11}C_4\), so it does not apply here. Exam tip: in this identity, add the upper indices and retain the common total lower index.

Related tags

Permutations And CombinationsVandermonde IdentityBinomial CoefficientsNcr SumCombinationsMathematicsClass 11 Mcq
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