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Binomial Theorem — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBinomial Theorem4 Marks
Question
In how many ways can one select a circket team of eleven from17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
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Answer

We have, There are total 5 bowlwrs and 12 batsm are avilable to select from. Number of ways to select a team and 11 that includes exactly 4 bowlers. = (7 batsm out of 12 bastsman) and (4 bowlers out of 5 bowlers) $={^{12}{\text{C}}}_{\text{7}}\times{^{5}{\text{C}}}_{\text{4}}$ $\Rightarrow \frac{12\times11\times10\times9\times8}{5\times4\times3\times2\times1}\times5$ $\Rightarrow 3960$

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